US20130072325A1

US20130072325A1 - Dimple patterns for golf balls

Info

Publication number: US20130072325A1
Application number: US13/675,041
Authority: US
Inventors: Michael R. Madson; Nicholas M. Nardacci
Original assignee: Acushnet Co
Current assignee: Acushnet Co
Priority date: 2008-10-31
Filing date: 2012-11-13
Publication date: 2013-03-21

Abstract

The present invention provides a method for arranging dimples on a golf ball surface in which the dimples are arranged in a pattern derived from at least one irregular domain generated from a regular or non-regular polyhedron, and particularly a dipyramid. The method includes choosing control points of a polyhedron, generating an irregular domain based on those control points, packing the irregular domain with dimples, and tessellating the irregular domain to cover the surface of the golf ball. The control points include the center of a polyhedral face, a vertex of the polyhedron, a midpoint or other point on an edge of the polyhedron and others. The method ensures that the symmetry of the underlying polyhedron is preserved while minimizing or eliminating great circles due to parting lines.

Description

CROSS-REFERENCE TO RELATED APPLICATIONS

This application is a continuation-in-part of U.S. patent application Ser. No. 13/667,175, filed Nov. 2, 2012, which is a continuation-in-part of U.S. patent application Ser. No. 13/252,260, filed Oct. 4, 2011, and U.S. patent application Ser. No. 13/046,823, filed Mar, 14, 2011, which is a continuation-in-part of U.S. patent application Ser. No. 12/262,464, filed Oct. 31, 2008, now U.S. Pat. No. 8,029,388, the entire disclosures of which are hereby incorporated herein by reference.

FIELD OF THE INVENTION

This invention relates to golf balls, particularly to golf balls possessing uniquely packed dimple patterns. More particularly, the invention relates to methods of arranging dimples on a golf ball by generating irregular domains based on polyhedrons, and particularly dipyramids, packing the irregular domains with dimples, and tessellating the domains onto the surface of the golf ball.

BACKGROUND OF THE INVENTION

Historically, dimple patterns for golf balls have had a variety of geometric shapes, patterns, and configurations. Primarily, patterns are laid out in order to provide desired performance characteristics based on the particular ball construction, material attributes, and player characteristics influencing the ball's initial launch angle and spin conditions. Therefore, pattern development is a secondary design step that is used to achieve the appropriate aerodynamic behavior, thereby tailoring ball flight characteristics and performance.
Aerodynamic forces generated by a ball in flight are a result of its velocity and spin. These forces can be represented by a lift force and a drag force. Lift force is perpendicular to the direction of flight and is a result of air velocity differences above and below the rotating ball. This phenomenon is attributed to Magnus, who described it in 1853 after studying the aerodynamic forces on spinning spheres and cylinders, and is described by Bernoulli's Equation, a simplification of the first law of thermodynamics. Bernoulli's equation relates pressure and velocity where pressure is inversely proportional to the square of velocity. The velocity differential, due to faster moving air on top and slower moving air on the bottom, results in lower air pressure on top and an upward directed force on the ball.
Drag is opposite in sense to the direction of flight and orthogonal to lift. The drag force on a ball is attributed to parasitic drag forces, which consist of pressure drag and viscous or skin friction drag. A sphere is a bluff body, which is an inefficient aerodynamic shape. As a result, the accelerating flow field around the ball causes a large pressure differential with high-pressure forward and low-pressure behind the ball. The low pressure area behind the ball is also known as the wake. In order to minimize pressure drag, dimples provide a means to energize the flow field and delay the separation of flow, or reduce the wake region behind the ball. Skin friction is a viscous effect residing close to the surface of the ball within the boundary layer.
The industry has seen many efforts to maximize the aerodynamic efficiency of golf balls, through dimple disturbance and other methods, though they are closely controlled by golf's national governing body, the United States Golf Association (U.S.G.A.). One U.S.G.A.
requirement is that golf balls have aerodynamic symmetry. Aerodynamic symmetry allows the ball to fly with a very small amount of variation no matter how the golf ball is placed on the tee or ground. Preferably, dimples cover the maximum surface area of the golf ball without detrimentally affecting the aerodynamic symmetry of the golf ball.
In attempts to improve aerodynamic symmetry, many dimple patterns are based on geometric shapes. These may include circles, hexagons, triangles, and the like. Other dimple patterns are based in general on the five Platonic Solids including icosahedron, dodecahedron, octahedron, cube, or tetrahedron. Yet other dimple patterns are based on the thirteen Archimedian Solids, such as the small icosidodecahedron, rhomicosidodecahedron, small rhombicuboctahedron, snub cube, snub dodecahedron, or truncated icosahedron. Furthermore, other dimple patterns are based on hexagonal dipyramids. Because the number of symmetric solid plane systems is limited, it is difficult to devise new symmetric patterns. Moreover, dimple patterns based on some of these geometric shapes result in less than optimal surface coverage and other disadvantageous dimple arrangements. Therefore, dimple properties such as number, shape, size, volume, and arrangement are often manipulated in an attempt to generate a golf ball that has improved aerodynamic properties.
U.S. Pat. No. 5,562,552 to Thurman discloses a golf ball with an icosahedral dimple pattern, wherein each triangular face of the icosahedron is split by three straight lines which each bisect a corner of the face to form three triangular faces for each icosahedral face, wherein the dimples are arranged consistently on the icosahedral faces.
U.S. Pat. No. 5,046,742 to Mackey discloses a golf ball with dimples packed into a 32-sided polyhedron composed of hexagons and pentagons, wherein the dimple packing is the same in each hexagon and in each pentagon.
U.S. Pat. No. 4,998,733 to Lee discloses a golf ball formed of ten “spherical” hexagons each split into six equilateral triangles, wherein each triangle is split by a bisecting line extending between a vertex of the triangle and the midpoint of the side opposite the vertex, and the bisecting lines are oriented to achieve improved symmetry.
U.S. Pat. No. 6,682,442 to Winfield discloses the use of polygons as packing elements for dimples to introduce predictable variance into the dimple pattern. The polygons extend from the poles of the ball to a parting line. Any space not filled with dimples from the polygons is filled with other dimples.

SUMMARY OF THE INVENTION

In one embodiment, the present invention is directed to a golf ball having an outer surface comprising a plurality of dimples. The dimples are arranged in multiple copies of an irregular domain covering the outer surface in a uniform pattern. The irregular domain is formed from a vertex to edge method based on an n-sided dipyramid projected on a sphere as n equally spaced lines of longitude from pole to pole bisected by a line around the equator to define a northern hemisphere and a southern hemisphere, the dimple pattern on the northern hemisphere being a mirror image of the dimple pattern on the southern hemisphere.
In another embodiment, the present invention is directed to a golf ball having an outer surface comprising a real parting line, a plurality of false parting lines, and a plurality of dimples. The dimples are arranged in a dimple pattern defined by tessellating an irregular domain to cover the outer surface in a uniform pattern. The irregular domain is bound by a segment and multiple copies thereof generated by a vertex to edge method based on an n-sided dipyramid. The segment and multiple copies thereof form the real and false parting lines of the ball.
In another embodiment, the present invention is directed to a method for arranging a plurality of dimples on a golf ball surface. The method comprises generating an irregular domain based on an n-sided dipyramid using a vertex to edge method, packing the irregular domain with dimples, and tessellating the irregular domain to cover the golf ball surface in a uniform pattern. The vertex to edge method comprises projecting the dipyramid onto a sphere, each face of the dipyramid having two side edges connected at a vertex at one end and connected by a base edge at the other end; connecting the vertex to a point P on the base edge with a non-straight segment; and patterning the segment in a manner to generate the irregular domain.

BRIEF DESCRIPTION OF THE DRAWINGS

In the accompanying drawings, which form a part of the specification and are to be read in conjunction therewith, and in which like reference numerals are used to indicate like parts in the various views:

FIG. 1A illustrates a golf ball having dimples arranged by a method of the present invention; FIG. 1B illustrates a polyhedron face; FIG. 1C illustrates an element of the present invention in the polyhedron face of FIG. 1B; FIG. 1D illustrates a domain formed by a methods of the present invention packed with dimples and formed from two elements of FIG. 1C;

FIG. 2 illustrates a single face of a polyhedron having control points thereon;

FIG. 3A illustrates a polyhedron face; FIG. 3B illustrates an element of the present invention packed with dimples; FIG. 3C illustrates a domain of the present invention packed with dimples formed from elements of FIG. 3B; FIG. 3D illustrates a golf ball formed by a method of the present invention formed of the domain of FIG. 3C;

FIG. 4A illustrates two polyhedron faces; FIG. 4B illustrates a first domain of the present invention in the two polyhedron faces of FIG. 4A; FIG. 4C illustrates a first domain and a second domain of the present invention in three polyhedron faces; FIG. 4D illustrates a golf ball formed by a method of the present invention formed of the domains of FIG. 4C;

FIG. 5A illustrates a polyhedron face; FIG. 5B illustrates a first domain of the present invention in a polyhedron face; FIG. 5C illustrates a first domain and a second domain of the present invention in three polyhedron faces; FIG. 5D illustrates a golf ball formed using a method of the present invention formed of the domains of FIG. 5C;

FIG. 6A illustrates a polyhedron face; FIG. 6B illustrates a portion of a domain of the present invention in the polyhedron face of FIG. 6A; FIG. 6C illustrates a domain formed by the methods of the present invention; FIG. 6D illustrates a golf ball formed using the methods of the present invention formed of domains of FIG. 6C;

FIG. 7A illustrates a polyhedron face; FIG. 7B illustrates a domain of the present invention in the polyhedron face of FIG. 7A; FIG. 7C illustrates a golf ball formed by a method of the present invention;

FIG.8A illustrates a first element of the present invention in a polyhedron face; FIG. 8B illustrates a first and a second element of the present invention in the polyhedron face of FIG. 8A; FIG. 8C illustrates two domains of the present invention composed of first and second elements of FIG. 8B; FIG. 8D illustrates a single domain of the present invention based on the two domains of FIG. 8C; FIG. 8E illustrates a golf ball formed using a method of the present invention formed of the domains of FIG. 8D;

FIG. 9A illustrates a polyhedron face; FIG. 9B illustrates an element of the present invention in the polyhedron face of FIG. 9A; FIG. 9C illustrates two elements of FIG. 9B combining to form a domain of the present invention;

FIG. 9D illustrates a domain formed by the methods of the present invention based on the elements of FIG. 9C; FIG. 9E illustrates a golf ball formed using a method of the present invention formed of domains of FIG. 9D;

FIG. 10A illustrates a face of a rhombic dodecahedron; FIG. 10B illustrates a segment of the present invention in the face of FIG. 10A; FIG. 10C illustrates the segment of FIG. 10B and copies thereof forming a domain of the present invention; FIG. 10D illustrates a domain formed by a method of the present invention based on the segments of FIG. 10C; and FIG. 10E illustrates a golf ball formed by a method of the present invention formed of domains of FIG. 10D.

FIG. 11A illustrates an octahedron face projected on a sphere; FIG. 11B illustrates a first domain of the present invention in the octahedron face of FIG. 11A; FIG. 11C illustrates a first domain and a second domain of the present invention projected on a sphere; FIG. 11D illustrates the domains of FIG. 11C tessellated to cover the surface of a sphere; FIG. 11E illustrates a portion of a golf ball formed using a method of the present invention; FIG. 11F illustrates another portion of a golf ball formed using a method of the present invention; and FIG. 11G illustrates a golf ball formed using a method of the present invention.

FIG. 12A illustrates an icosahedron face projected on a sphere; FIG. 12B illustrates a first domain of the present invention in the icosahedron face of FIG. 12A; FIG. 12C illustrates a first domain and a second domain of the present invention projected on a sphere; FIG. 12D illustrates the domains of FIG. 12C tessellated to cover the surface of a sphere; FIG. 12E illustrates a portion of a golf ball formed using a method of the present invention; FIG. 12F illustrates another portion of a golf ball formed using a method of the present invention; and FIG. 12G illustrates a golf ball formed using a method of the present invention.

FIG. 13A illustrates a cube face projected on a sphere; FIG. 13B illustrates a first domain of the present invention in the cube face of FIG. 13A; FIG. 13C illustrates a first domain and a second domain of the present invention projected on a sphere; FIG. 13D illustrates the domains of FIG. 13C tessellated to cover the surface of a sphere; FIG. 13E illustrates a first domain of the present invention packed with dimples; FIG. 13F illustrates a second domain of the present invention packed with dimples; and FIG. 13G illustrates a golf ball formed using a method of the present invention.

FIG. 14A illustrates a six-sided dipyramid projected on a sphere; FIG. 14B illustrates a segment in a face of the dipyramid of FIG. 14A according to one embodiment of the present invention; FIG. 14C illustrates an irregular domain generated according to one embodiment of the present invention; FIG. 14D illustrates an irregular domain generated according to another embodiment of the present invention; FIG. 14E illustrates the irregular domain of FIG. 14C packed with dimples; FIG. 14F illustrates the irregular domain of FIG. 14D packed with dimples; FIG. 14G illustrates a golf ball formed using a method according to one embodiment of the present invention; and FIG. 14H illustrates a golf ball formed using a method according to another embodiment of the present invention.

DETAILED DESCRIPTION

The present invention provides a method for arranging dimples on a golf ball surface in a pattern derived from at least one irregular domain generated from a regular or non-regular polyhedron. The method includes choosing control points of a polyhedron, connecting the control points with a non-straight sketch line, patterning the sketch line in a first manner to generate an irregular domain, optionally patterning the sketch line in a second manner to create an additional irregular domain, packing the irregular domain(s) with dimples, and tessellating the irregular domain(s) to cover the surface of the golf ball in a uniform pattern. The control points include the center of a polyhedral face, a vertex of the polyhedron, a midpoint or other point on an edge of the polyhedron, and others. The method ensures that the symmetry of the underlying polyhedron is preserved while minimizing or eliminating great circles due to parting lines from the molding process.
In a particular embodiment, illustrated in FIG. 1A, the present invention comprises a golf ball 10 comprising dimples 12. Dimples 12 are arranged by packing irregular domains 14 with dimples, as seen best in FIG. 1D. Irregular domains 14 are created in such a way that, when tessellated on the surface of golf ball 10, they impart greater orders of symmetry to the surface than prior art balls. The irregular shape of domains 14 additionally minimize the appearance and effect of the golf ball parting line from the molding process, and allows greater flexibility in arranging dimples than would be available with regularly shaped domains.
For purposes of the present invention, the term “irregular domains” refers to domains wherein at least one, and preferably all, of the segments defining the borders of the domain is not a straight line.
The irregular domains can be defined through the use of any one of the exemplary methods described herein. In one embodiment, the method produces one or more unique domains based on circumscribing a sphere with the vertices of a regular polyhedron. The vertices of the circumscribed sphere based on the vertices of the corresponding polyhedron with origin (0,0,0) are defined below in Table 1.

TABLE 1

Vertices of Circumscribed Sphere based on
Corresponding Polyhedron Vertices

Type of
Polyhedron	Vertices

Tetrahedron	(+1, +1, +1); (−1, −1, +1); (−1, +1, −1); (+1, −1, −1)
Cube	(±1, ±1, ±1)
Octahedron	(±1, 0, 0); (0, ±1, 0); (0, 0, ±1)
Dodecahedron	(±1, ±1, ±1); (0, ±1/φ, ±φ); (±1/φ, ±φ, 0); (±φ, 0, ±1/φ)*
Icosahedron	(0, ±1, ±φ); (±1, ±φ, 0); (±φ, 0, ±1)*

*φ = (1 + {square root over (5)})/2

In another embodiment, the method produces a unique domain based on projecting a dipyramid on a sphere.
Each method has a unique set of rules which are followed for the domain to be symmetrically patterned on the surface of the golf ball. Each method is defined by the combination of at least two control points. These control points, which are taken from one or more faces of a regular or non-regular polyhedron, include at least the following types: the center C of a polyhedron face; a vertex V of a face of a regular polyhedron; the midpoint M of an edge of a face of the polyhedron; a vertex V of a dipyramid; and a point P on an edge E of the base of a dipyramid.
FIG. 2 shows an exemplary face 16 of a polyhedron (a regular dodecahedron in this case) and one of each a center C, a midpoint M, a vertex V, and an edge E on face 16. The two control points C, M, or V may be of the same or different types. Accordingly, six types of methods for use with regular polyhedrons are defined as follows:

- 1. Center to midpoint (C→M);
- 2. Center to center (C→C);
- 3. Center to vertex (C→V);
- 4. Midpoint to midpoint (M→M);
- 5. Midpoint to Vertex (M→V); and
- 6. Vertex to Vertex (V→V).

FIG. 14B shows an exemplary dipyramid, a vertex V of the dipyramid, and a point P on an edge E of the base of the dipyramid. Thus, one type of method for use with dipyramids is defined as the vertex to edge method (V→E).
While each method differs in its particulars, they all follow the same basic scheme. First, a non-linear sketch line is drawn connecting the two control points. This sketch line may have any shape, including, but not limited, to an arc, a spline, two or more straight or arcuate lines or curves, or a combination thereof. Second, the sketch line is patterned in a method specific manner to create a domain, as discussed below. Third, when necessary, the sketch line is patterned in a second fashion to create a second domain.
While the basic scheme is consistent for each of the six methods, each method preferably follows different steps in order to generate the domains from a sketch line between the two control points, as described below with reference to each of the methods individually.

The Center to Vertex Method

Referring again to FIGS. 1A-1D, the center to vertex method yields one domain that tessellates to cover the surface of golf ball 10. The domain is defined as follows:

- 1. A regular polyhedron is chosen (FIGS. 1A-1D use an icosahedron);
- 2. A single face 16 of the regular polyhedron is chosen, as shown in FIG. 1B;
- 3. Center C of face 16, and a first vertex V₁of face 16 are connected with any non-linear sketch line, hereinafter referred to as a segment 18;
- 4. A copy 20 of segment 18 is rotated about center C, such that copy 20 connects center C with vertex V₂adjacent to vertex V₁. The two segments 18 and 20 and the edge E connecting vertices V₁and V₂define an element 22, as shown best in FIG. 1C; and
- 5. Element 22 is rotated about midpoint M of edge E to create a domain 14, as shown best in FIG. 1D.

When domain 14 is tessellated to cover the surface of golf ball 10, as shown in FIG. 1A, a different number of total domains 14 will result depending on the regular polyhedron chosen as the basis for control points C and V₁. The number of domains 14 used to cover the surface of golf ball 10 is equal to the number of faces P_Fof the polyhedron chosen times the number of edges P_Eper face of the polyhedron divided by 2, as shown below in Table 2.

TABLE 2

Domains Resulting From Use of Specific Polyhedra
When Using the Center to Vertex Method

	Number of	Number of	Number of
Type of Polyhedron	Faces, P_F	Edges, P_E	Domains 14

Tetrahedron	4	3	6
Cube	6	4	12
Octahedron	8	3	12
Dodecahedron	12	5	30
Icosahedron	20	3	30

The Center to Midpoint Method

Referring to FIGS. 3A-3D, the center to midpoint method yields a single irregular domain that can be tessellated to cover the surface of golf ball 10. The domain is defined as follows:

- 1. A regular polyhedron is chosen (FIGS. 3A-3D use a dodecahedron);
- 2. A single face 16 of the regular polyhedron is chosen, as shown in FIG. 3A;
- 3. Center C of face 16, and midpoint M₁of a first edge E_lof face 16 are connected with a segment 18;
- 4. A copy 20 of segment 18 is rotated about center C, such that copy 20 connects center C with a midpoint M₂of a second edge E₂adjacent to first edge E₁. The two segments 16 and 18 and the portions of edge E₁and edge E₂between midpoints M₁and M₂define an element 22; and
- 5. Element 22 is patterned about vertex V of face 16 which is contained in element 22 and connects edges E₁and E₂to create a domain 14.

When domain 14 is tessellated around a golf ball 10 to cover the surface of golf ball 10, as shown in FIG. 3D, a different number of total domains 14 will result depending on the regular polyhedron chosen as the basis for control points C and M₁. The number of domains 14 used to cover the surface of golf ball 10 is equal to the number of vertices P_Vof the chosen polyhedron, as shown below in Table 3.

TABLE 3

Domains Resulting From Use of Specific Polyhedra
When Using the Center to Midpoint Method

Type of Polyhedron	Number of Verticles, P_V	Number of Domains 14

Tetrahedron	4	4
Cube	8	8
Octahedron	6	6
Dodecahedron	20	20
Icosahedron	12	12

The Center to Center Method

Referring to FIGS. 4A-4D, the center to center method yields two domains that can be tessellated to cover the surface of golf ball 10. The domains are defined as follows:

- 1. A regular polyhedron is chosen (FIGS. 4A-4D use a dodecahedron);
- 2. Two adjacent faces 16 a and 16 b of the regular polyhedron are chosen, as shown in FIG. 4A;
- 3. Center C₁of face 16 a, and center C₂of face 16 b are connected with a segment 18;
- 4. A copy 20 of segment 18 is rotated 180 degrees about the midpoint M between centers C₁and C₂, such that copy 20 also connects center C₁with center C₂, as shown in FIG. 4B. The two segments 16 and 18 define a first domain 14 a; and
- 5. Segment 18 is rotated equally about vertex V to define a second domain 14 b, as shown in FIG. 4C.

When first domain 14 a and second domain 14 b are tessellated to cover the surface of golf ball 10, as shown in FIG. 4D, a different number of total domains 14 a and 14 b will result depending on the regular polyhedron chosen as the basis for control points C₁and C₂. The number of first and second domains 14 a and 14 b used to cover the surface of golf ball 10 is P_F*P_E/2 for first domain 14 a and P_Vfor second domain 14 b, as shown below in Table 4.

TABLE 4

Domains Resulting From Use of Specific Polyhedra
When Using the Center to Center Method

	Number	Number of	Number	Number	Number of
	of	First	of	of	Second
Type of	Vertices,	Domains	Faces,	Edges,	Domains
Polyhedron	P
_V	14a	P_F	P_E	14b

Tetrahedron	4	6	4	3	4
Cube	8	12	6	4	8
Octahedron	6	9	8	3	6
Dodecahedron	20	30	12	5	20
Icosahedron	12	18	20	3	12

The Midpoint to Midpoint Method

Referring to FIGS. 5A-5D, 11A-11G, 12A-12G and 13A-13G, the midpoint to midpoint method yields two domains that tessellate to cover the surface of golf ball 10. The domains are defined as follows:

- 1. A regular polyhedron is chosen (FIGS. 5A-5D use a dodecahedron, FIGS. 11A-11G use an octahedron, FIGS. 12A-12G use an icosahedron, FIGS. 13A-13G use a cube);
- 2. A single face 16 of the regular polyhedron is projected onto a sphere, as shown in FIGS. 5A, 11A, 12A and 13A;
- 3. The midpoint M₁of a first edge E₁of face 16, and the midpoint M₂of a second edge E₂adjacent to first edge E₁are connected with a segment 18, as shown in FIGS. 5A, 11A, 12A and 13A;
- 4. Segment 18 is patterned around center C of face 16, at an angle of rotation equal to 360/P_E, to form a first domain 14 a, as shown in FIGS. 5B, 11B, 12B and 13B;
- 5. Segment 18, along with the portions of first edge E₁and second edge E₂between midpoints M₁and M₂, define an element 22, as shown in FIGS. 5B, 11B, 12B and 13B; and
- 6. Element 22 is patterned about the vertex V which connects edges E₁and E₂to create a second domain 14 b, as shown in FIGS. 5C, 11C, 12C and 13C (in FIGS. 12C, 12D and 13D, each section of the second domain is designated 14 b). The number of segments in the pattern that forms the second domain is equal to P_F*P_E/P_V.

When first domain 14 a and second domain 14 b are tessellated to cover the surface of golf ball 10, as shown in FIGS. 5D, 11D, 12D and 13D, a different number of total domains 14 a and 14 b will result depending on the regular polyhedron chosen as the basis for control points M₁and M₂. The number of first and second domains 14 a and 14 b used to cover the surface of golf ball 10 is P_Ffor first domain 14 a and P_Vfor second domain 14 b, as shown below in Table 5.
In a particular aspect of the embodiment shown in FIGS. 11A-11G, segment 18 forms a portion of a real or false parting line of golf ball 10. Thus, segment 18, along with each copy thereof that is produced by steps 4 and 6 above, produce the real and three false parting lines of the ball when the domains are tessellated to cover the ball's surface.
In a particular aspect of the embodiment shown in FIGS. 12A-12G, segment 18, along with each copy thereof that is produced by steps 4 and 6 above, produce the real parting line and five false parting lines of the ball when the domains are tessellated to cover the ball's surface.
In a particular aspect of the embodiment shown in FIGS. 13A-13G, segment 18, along with each copy thereof that is produced by steps 4 and 6 above, produce the real parting line and three false parting lines of the ball when the domains are tessellated to cover the ball's surface.

TABLE 5

Domains Resulting From Use of Specific Polyhedra
When Using the Midpoint to Midpoint Method

		Number of		Number of
Type of	Number of	First	Number of	Second
Polyhedron	Faces, P_F	Domains14a	Vertices, P_V	Domains 14b

Tetrahedron

	4	4	4	4
Cube	6	6	8	8
Octahedron	8	8	6	6
Dodecahedron	12	12	20	20
Icosahedron	20	20	12	12

The Midpoint to Vertex Method

Referring to FIGS. 6A-6D, the midpoint to vertex method yields one domain that tessellates to cover the surface of golf ball 10. The domain is defined as follows:

- 1. A regular polyhedron is chosen (FIGS. 6A-6D use a dodecahedron);
- 2. A single face 16 of the regular polyhedron is chosen, as shown in FIG. 6A;
- 3. A midpoint M₁of edge E₁of face 16 and a vertex V₁on edge E₁are connected with a segment 18;
- 4. Copies 20 of segment 18 is patterned about center C of face 16, one for each midpoint M₂and vertex V₂of face 16, to define a portion of domain 14, as shown in FIG. 6B; and
- 5. Segment 18 and copies 20 are then each rotated 180 degrees about their respective midpoints to complete domain 14, as shown in FIG. 6C.

When domain 14 is tessellated to cover the surface of golf ball 10, as shown in FIG. 6D, a different number of total domains 14 will result depending on the regular polyhedron chosen as the basis for control points M₁and V₁. The number of domains 14 used to cover the surface of golf ball 10 is P_F, as shown in Table 6.

TABLE 6

Domains Resulting From Use of Specific Polyhedra
When Using the Midpoint to Vertex Method

Type of Polyhedron	Number of Faces, P_F	Number of Domains 14

Tetrahedron	4	4
Cube	6	6
Octahedron	8	8
Dodecahedron	12	12
Icosahedron	20	20

The Vertex to Vertex Method

Referring to FIGS. 7A-7C, the vertex to vertex method yields two domains that tessellate to cover the surface of golf ball 10. The domains are defined as follows:

- 1. A regular polyhedron is chosen (FIGS. 7A-7C use an icosahedron);
- 2. A single face 16 of the regular polyhedron is chosen, as shown in FIG. 7A;
- 3. A first vertex V₁face 16, and a second vertex V₂adjacent to first vertex V₁are connected with a segment 18;
- 4. Segment 18 is patterned around center C of face 16 to form a first domain 14 a, as shown in FIG. 7B;
- 5. Segment 18, along with edge E₁between vertices V₁and V₂, defines an element 22; and
- 6. Element 22 is rotated around midpoint M₁of edge E₁to create a second domain 14 b.

When first domain 14 a and second domain 14 b are tessellated to cover the surface of golf ball 10, as shown in FIG. 7C, a different number of total domains 14 a and 14 b will result depending on the regular polyhedron chosen as the basis for control points V₁and V₂. The number of first and second domains 14 a and 14 b used to cover the surface of golf ball 10 is P_Ffor first domain 14 a and P_F*P_E/2 for second domain 14 b, as shown below in Table 7.

TABLE 7

Domains Resulting From Use of Specific Polyhedra
When Using the Vertex to Vertex Method

	Number	Number of	Number of	Number of
Type of	of	First	Edges per	Second
Polyhedron	Faces, P_F	Domains 14a	Face, P_E	Domains 14b

Tetrahedron

	4	4	3	6
Cube	6	6	4	12
Octahedron	8	8	3	12
Dodecahedron	12	12	5	30
Icosahedron	20	20	3	30

While the six methods previously described each make use of two control points, it is possible to create irregular domains based on more than two control points. For example, three, or even more, control points may be used. The use of additional control points allows for potentially different shapes for irregular domains. An exemplary method using a midpoint M, a center C and a vertex V as three control points for creating one irregular domain is described below.

The Midpoint to Center to Vertex Method

Referring to FIGS. 8A-8E, the midpoint to center to vertex method yields one domain that tessellates to cover the surface of golf ball 10. The domain is defined as follows:

- 1. A regular polyhedron is chosen (FIGS. 8A-8E use an icosahedron);
- 2. A single face 16 of the regular polyhedron is chosen, as shown in FIG. 8A;
- 3. A midpoint M₁on edge E₁of face 16, Center C of face 16 and a vertex V₁on edge E₁are connected with a segment 18, and segment 18 and the portion of edge E₁between midpoint M₁and vertex V₁define a first element 22 a, as shown in FIG. 8A;
- 4. A copy 20 of segment 18 is rotated about center C, such that copy 20 connects center C with a midpoint M₂on edge E₂adjacent to edge E₁, and connects center C with a vertex V₂at the intersection of edges E₁and E₂, and the portion of segment 18 between midpoint M₁and center C, the portion of copy 20 between vertex V₂and center C, and the portion of edge E₁between midpoint M₁and vertex V₂define a second element 22 b, as shown in FIG. 8B;
- 5. First element 22 a and second element 22 b are rotated about midpoint M₁of edge E₁, as seen in FIGS. 8C, to define two domains 14, wherein a single domain 14 is bounded solely by portions of segment 18 and copy 20 and the rotation 18′ of segment 18, as seen in FIG. 8D.

When domain 14 is tessellated to cover the surface of golf ball 10, as shown in FIG. 8E, a different number of total domains 14 will result depending on the regular polyhedron chosen as the basis for control points M, C, and V. The number of domains 14 used to cover the surface of golf ball 10 is equal to the number of faces P_Fof the polyhedron chosen times the number of edges P_Eper face of the polyhedron, as shown below in Table 8.

TABLE 8

Domains Resulting From Use of Specific Polyhedra
When Using the Midpoint to Center to Vertex Method

Type of	Number of	Number of	Number of
Polyhedron	Faces, P_F	Edges, P_E	Domains 14

Tetrahedron	4	3	12
Cube	6	4	24
Octahedron	8	3	24
Dodecahedron	12	5	60
Icosahedron	20	3	60

While the methods described previously provide a framework for the use of center C, vertex V, and midpoint M as the only control points, other control points are useable. For example, a control point may be any point P on an edge E of the chosen polyhedron face. When this type of control point is used, additional types of domains may be generated, though the mechanism for creating the irregular domain(s) may be different. An exemplary method, using a center C and a point P on an edge, for creating one such irregular domain is described below.

The Center to Edge Method

Referring to FIGS. 9A-9E, the center to edge method yields one domain that tessellates to cover the surface of golf ball 10. The domain is defined as follows:

- 1. A regular polyhedron is chosen (FIGS. 9A-9E use an icosahedron);
- 2. A single face 16 of the regular polyhedron is chosen, as shown in FIG. 9A;
- 3. Center C of face 16, and a point P₁on edge E₁are connected with a segment 18;
- 4. A copy 20 of segment 18 is rotated about center C, such that copy 20 connects center C with a point P₂on edge E₂adjacent to edge E₁, where point P₂is positioned identically relative to edge E₂as point P₁is positioned relative to edge E₁, such that the two segments 18 and 20 and the portions of edges E₁and E₂between points P₁and P₂, respectively, and a vertex V, which connects edges E₁and E₂, define an element 22, as shown best in FIG. 9B; and
- 5. Element 22 is rotated about midpoint M₁of edge E₁or midpoint M₂of edge E₂, whichever is located within element 22, as seen in FIGS. 9B-9C, to create a domain 14, as seen in FIG. 9D.

When domain 14 is tessellated to cover the surface of golf ball 10, as shown in FIG. 9E, a different number of total domains 14 will result depending on the regular polyhedron chosen as the basis for control points C and P₁. The number of domains 14 used to cover the surface of golf ball 10 is equal to the number of faces P_Fof the polyhedron chosen times the number of edges P_Eper face of the polyhedron divided by 2, as shown below in Table 9.

TABLE 9

Domains Resulting From Use of Specific Polyhedra
When Using the Center to Edge Method

Though each of the above described methods has been explained with reference to regular polyhedrons, they may also be used with certain non-regular polyhedrons, such as Archimedean Solids, Catalan Solids, or others. The methods used to derive the irregular domains will generally require some modification in order to account for the non-regular face shapes of the non-regular solids. An exemplary method for use with a Catalan Solid, specifically a rhombic dodecahedron, is described below.

A Vertex to Vertex Method for a Rhombic Dodecahedron

Referring to FIGS. 10A-10E, a vertex to vertex method based on a rhombic dodecahedron yields one domain that tessellates to cover the surface of golf ball 10. The domain is defined as follows:

- 1. A single face 16 of the rhombic dodecahedron is chosen, as shown in FIG. 10A;
- 2. A first vertex V₁face 16, and a second vertex V₂adjacent to first vertex V₁are connected with a segment 18, as shown in FIG. 10B;
- 3. A first copy 20 of segment 18 is rotated about vertex V₂, such that it connects vertex V₂to vertex V3 of face 16, a second copy 24 of segment 18 is rotated about center C, such that it connects vertex V₃and vertex V₄of face 16, and a third copy 26 of segment 18 is rotated about vertex V₁such that it connects vertex V₁to vertex V₄, all as shown in FIG. 10C, to form a domain 14, as shown in FIG. 10D;

When domain 14 is tessellated to cover the surface of golf ball 10, as shown in FIG. 10E, twelve domains will be used to cover the surface of golf ball 10, one for each face of the rhombic dodecahedron.

A Vertex to Edge Method for a Dipyramid

Referring to FIGS. 14A-14H, the vertex to edge method yields one domain that tessellates to cover the surface of golf ball 10. The domain is defined as follows:

- 1. An n-sided dipyramid, having a total number of faces equal to 2n, is projected on a sphere as n equally spaced lines of longitude going from pole to pole bisected by a line around the equator defining a northern hemisphere and a southern hemisphere. In FIGS. 14A-14H, n=6. As shown in FIG. 14A, each face 16 of the dipyramid has two side edges S₁and S₂connected at a vertex V at one end and connected by a base edge E at the other end.
- 2. As shown in FIG. 14B, a single face 16 of the dipyramid is chosen and the vertex V of face 16 is connected to a point P on the base edge E of face 16 with a segment 18.
- 3. Segment 18 is patterned in a manner to generate an irregular domain 14.
  - a. In the embodiment shown in FIG. 14C, irregular domain 14 is generated by mirroring segment 18 about the base edge E to define copy 18 a of segment 18, and rotating segment 18 and copy 18 a about an axis connecting vertex V to the origin of the sphere to define copy 18 b and copy 18 c. The angle of rotation is equal to 360/n. In FIG. 14C, each section of the domain is designated 14.
  - b. In the embodiment shown in FIG. 14D, irregular domain 14 is generated by patterning segment 18 180° about an axis connecting point P with the center of the sphere to define copy 18 a, and rotating segment 18 and copy 18 a about an axis connecting vertex V to the origin of the sphere to define copy 18 b and copy 18 c. The angle of rotation is equal to 360/n. In FIG. 14D, each section of the domain is designated 14.

The irregular domain 14 is tessellated to cover the surface of the ball, as shown in FIGS. 14C and 14D, by patterning the domain n times about the center axis.
In a particular embodiment of the vertex to edge method for an n-sided dipyramid, the dipyramid has an even number of sides, and segment 18 forms a portion of a real or false parting line of golf ball 10. Thus, segment 18, along with each copy thereof that is produced by step 3 above, produce one real and multiple false parting lines of the ball, the number of false parting lines being equal to (ⁿ/₂)−1, and n being≧4, or ≧6, or >6.
After the irregular domain(s) are created using any of the above methods, the domain(s) may be packed with dimples in order to be usable in creating golf ball 10. In FIGS. 11E-11G, a first domain and a second domain are created using the midpoint to midpoint method based on an octahedron. FIG. 11E shows a first domain 14 a and a portion of a second domain 14 b packed with dimples, with the dimples of the first domain 14 a designated by the letter a. FIG. 11F shows a second domain 14 b and a portion of a first domain 14 a packed with dimples, with the dimples of the second domain 14 b designated by the letter b. FIG. 11G shows a first domain 14 a and a second domain 14 b packed with dimples and tessellated to cover the surface of golf ball 10. In FIGS. 12E-12G, a first domain and a second domain are created using the midpoint to midpoint method based on an icosahedron. FIG. 12E shows a first domain 14 a and a second domain 14 b packed with dimples, with the dimples of the first domain 14 a designated by the letter a. FIG. 12F shows a second domain 14 b and a first domain 14 a packed with dimples, with the dimples of the second domain 14 b designated by the letter b. FIG. 12G shows a first domain and a second domain packed with dimples and tessellated to cover the surface of golf ball 10. In FIGS. 13E-13G, a first domain and a second domain are created using the midpoint to midpoint method based on a cube. FIG. 13E shows a first domain 14 a packed with dimples and a second domain 14 b. FIG. 13F shows a second domain 14 b packed with dimples and a first domain 14 a. FIG. 13G shows a first domain and a second domain packed with dimples and tessellated to cover the surface of golf ball 10. FIGS. 14C-14H show a domain created using the vertex to edge method for a six-sided dipyramid. FIG. 14E shows the domain of FIG. 14C packed with dimples. FIG. 14F shows the domain of FIG. 14D packed with dimples. FIG. 14G shows the domain of FIG. 14C packed with dimples and patterned six times about the center axis to cover the surface of golf ball 10. FIG. 14H shows the domain of FIG. 14D packed with dimples and patterned six times about the center axis to cover the surface of golf ball 10. In a particular embodiment of the present invention, the dimple pattern on the northern hemisphere is a minor image of the dimple pattern on the southern hemisphere, as shown in FIGS. 14E and 14G.
In one embodiment, there are no limitations on how the dimples are packed. In another embodiment, the dimples are packed such that no dimple intersects a line segment.
There are no limitations to the dimple shapes or profiles selected to pack the domains. Though the present invention includes substantially circular dimples in one embodiment, dimples or protrusions (brambles) having any desired characteristics and/or properties may be used. For example, in one embodiment the dimples may have a variety of shapes and sizes including different depths and perimeters. In particular, the dimples may be concave hemispheres, or they may be triangular, square, hexagonal, catenary, polygonal or any other shape known to those skilled in the art. They may also have straight, curved, or sloped edges or sides. To summarize, any type of dimple or protrusion (bramble) known to those skilled in the art may be used with the present invention. The dimples may all fit within each domain, as seen in FIGS. 1A, 1D, 11E-11G, 12E-12G, 13E-G, 14E-H, or dimples may be shared between one or more domains, as seen in FIGS. 3C-3D, so long as the dimple arrangement on each independent domain remains consistent across all copies of that domain on the surface of a particular golf ball. Alternatively, the tessellation can create a dimple pattern that covers more than about 60%, preferably more than about 70%, and more preferably more than about 80% of the golf ball surface.
In other embodiments, the domains may not be packed with dimples, and the borders of the irregular domains may instead comprise ridges or channels. In golf balls having this type of irregular domain, the one or more domains or sets of domains preferably overlap to increase surface coverage of the channels. Alternatively, the borders of the irregular domains may comprise ridges or channels and the domains are packed with dimples.
When the domain(s) is patterned onto the surface of a golf ball, the arrangement of the domains dictated by their shape and the underlying polyhedron ensures that the resulting golf ball has a high order of symmetry, equaling or exceeding 12. The order of symmetry of a golf ball produced using the method of the current invention will depend on the regular or non-regular polygon on which the irregular domain is based. The order and type of symmetry for golf balls produced based on the five regular polyhedra are listed below in Table 10.

TABLE 10

Symmetry of Golf Ball of the Present Invention
as a Function of Polyhedron

Type of		Symmetrical
Polyhedron	Type of Symmetry	Order

Tetrahedron	Chiral Tetrahedral Symmetry	12
Cube	Chiral Octahedral Symmetry	24
Octahedron	Chiral Octahedral Symmetry	24
Dodecahedron	Chiral Icosahedral Symmetry	60
Icosahedron	Chiral Icosahedral Symmetry	60

These high orders of symmetry have several benefits, including more even dimple distribution, the potential for higher packing efficiency, and improved means to mask the ball parting line. Further, dimple patterns generated in this manner may have improved flight stability and symmetry as a result of the higher degrees of symmetry.
In other embodiments, the irregular domains do not completely cover the surface of the ball, and there are open spaces between domains that may or may not be filled with dimples. This allows dissymmetry to be incorporated into the ball.
Dimple patterns of the present invention are particularly suitable for packing dimples on seamless golf balls. Seamless golf balls and methods of producing such are further disclosed, for example, in U.S. Pat. Nos. 6,849,007 and 7,422,529, the entire disclosures of which are hereby incorporated herein by reference.
When numerical lower limits and numerical upper limits are set forth herein, it is contemplated that any combination of these values may be used.
All patents, publications, test procedures, and other references cited herein, including priority documents, are fully incorporated by reference to the extent such disclosure is not inconsistent with this invention and for all jurisdictions in which such incorporation is permitted.
While the illustrative embodiments of the invention have been described with particularity, it will be understood that various other modifications will be apparent to and can be readily made by those of ordinary skill in the art without departing from the spirit and scope of the invention. Accordingly, it is not intended that the scope of the claims appended hereto be limited to the examples and descriptions set forth herein, but rather that the claims be construed as encompassing all of the features of patentable novelty which reside in the present invention, including all features which would be treated as equivalents thereof by those of ordinary skill in the art to which the invention pertains.

Claims

What is claimed is:

1. A golf ball having an outer surface comprising a plurality of dimples arranged in multiple copies of an irregular domain covering the outer surface in a uniform pattern, wherein the irregular domain is formed from a vertex to edge method based on an n-sided dipyramid projected on a sphere as n equally spaced lines of longitude from pole to pole bisected by a line around the equator to define a northern hemisphere and a southern hemisphere, wherein the dimple pattern on the northern hemisphere is a mirror image of the dimple pattern on the southern hemisphere.

2. The golf ball of claim 1, wherein the outer surface of the golf ball comprises 342 dimples.

3. The golf ball of claim 1, wherein the outer surface of the golf ball comprises 328 dimples.

4. The golf ball of claim 1, wherein the golf ball has a planar parting line along the equator.

5. The golf ball of claim 1, wherein the golf ball has a non-planar parting line defined by portions of the boundary of the irregular domain.

6. A golf ball having an outer surface comprising a plurality of dimples arranged in a dimple pattern defined by tessellating an irregular domain to cover the outer surface in a uniform pattern, the irregular domain being bound by a segment and multiple copies thereof generated by a vertex to edge method based on an n-sided dipyramid, wherein the segment and multiple copies thereof produce one real and multiple false parting lines of the ball.

7. The golf ball of claim 6, wherein the dipyramid is projected on a sphere as n equally spaced lines of longitude from pole to pole bisected by a line around the equator to define a northern hemisphere and a southern hemisphere, and wherein the dimple pattern on the northern hemisphere is a mirror image of the dimple pattern on the southern hemisphere.

8. The golf ball of claim 6, wherein the outer surface of the golf ball comprises 342 dimples.

9. The golf ball of claim 6, wherein the outer surface of the golf ball comprises 328 dimples.

10. The golf ball of claim 6, wherein the number of false parting lines is equal to (ⁿ/₂)−1, and wherein n is an even number greater than or equal to 4.

11. The golf ball of claim 6, wherein the number of false parting lines is equal to (ⁿ/₂)−1, and wherein n is an even number greater than or equal to 6.

12. The golf ball of claim 6, wherein the number of false parting lines is equal to (ⁿ/₂)−1, and wherein n is an even number greater than or equal to 8.

13. A method for arranging a plurality of dimples on a golf ball surface, the method comprising:

generating an irregular domain based on an n-sided dipyramid using a vertex to edge method, the vertex to edge method comprising:

projecting the dipyramid onto a sphere, each face of the dipyramid having two side edges connected at a vertex at one end and connected by a base edge at the other end;

connecting the vertex to a point P on the base edge with a non-straight segment; and

patterning the segment in a manner to generate the irregular domain;

packing the irregular domain with dimples; and

tessellating the irregular domain to cover the golf ball surface in a uniform pattern.

14. The method of claim 13, wherein the irregular domain is generated by mirroring a first copy of the segment about the base edge and rotating an additional copy of the segment and the first copy about an axis connecting the vertex to the origin of the sphere, wherein the angle of rotation is equal to 360/n.

15. The method of claim 14, wherein the segment, first copy, and additional copy produce one real and multiple false parting lines of the ball.

16. The method of claim 15, wherein the number of false parting lines is equal to (ⁿ/₂)−1, and wherein n is an even number greater than or equal to 4.

17. The method of claim 15, wherein the number of false parting lines is equal to (ⁿ/₂)−1, and wherein n is an even number greater than or equal to 8.

18. The method of claim 13, wherein the irregular domain is generated by rotating a first copy of the segment 180° about an axis connecting point P with the origin of the sphere and rotating an additional copy of the segment and the first copy about an axis connecting the vertex to the origin of the sphere, wherein the angle of rotation is equal to 360/n.

19. The method of claim 18, wherein the segment, first copy, and additional copy produce one real and multiple false parting lines of the ball.

20. The method of claim 19, wherein the number of false parting lines is equal to (ⁿ/₂)−1, and wherein n is an even number greater than or equal to 4.

21. The method of claim 19, wherein the number of false parting lines is equal to (ⁿ/₂)−1, and wherein n is an even number greater than or equal to 8.