in fig1 there is shown the cross .- sectional configuration of a conventional circular dimple 2 in the surface of a golf ball 4 . the dimple has a diameter d and a depth d . a circular dimple can be thought of as being created by the intersection of a spherical surface with the surface of a golf ball , with the radius of the dimple being defined by the radius of the sphere . the present invention relates to non - circular dimple geometries formed by intersecting surfaces , such as for example , cylindrical and planar surfaces . intersecting cylinders form tri - cylinders , tri - semicylinders , bi - cylinders , quad - semicylinders or more generally n - cylinders . dimple volumes are formed by the intersecting n cylinders , with their long axes coplanar and equal angles between those long axes . as will be developed in detail below , the intersecting cylinders may have a pair of smaller cylinders tangent to the larger cylinder on each side to form edge radii of the dimple . this is similar to a dual radius dimple profile . a dual radius dimple is formed with a larger spherical radius ( as the bottom of the dimple ) tangent to a torus of smaller radius ( forming an edge radius ). the dual radius n - cylinder dimple bottom is formed by n cylinders and the edge radius is formed by a pair of smaller cylinders tangent to each of the larger cylinders . these are called dual radius tri - cylinders , tri - semicylinders , bi - cylinders , and quad - semicylinders . the dimples volumes are formed by the intersecting n cylinders ( each with a pair of smaller tangent cylinders ), with their long axes coplanar and equal angles between those long axes . if the radii of the cylinders used to form these shapes are the same , the shape is regular . two dimensional cross - sections of these volumes ( cut parallel to the plane of the long axes ) are regular 2n - gons , e . g . a regular polygon of 2 × n sides . examples of the geometries used to create dimples in accordance with the invention are shown in fig2 , and 4 . more particularly , fig2 shows the geometry defined by the intersection of three cylinders of the same diameter and is referred to as a symmetric tri - cylinder 6 . the hexagonal prism circumscribed by the tri - cylinder is shown in phantom . tri - cylinders are formed from three cylinders oriented 120 □ apart with a common axis of rotation central to the dimple volume . the configuration of the two - dimensional cross - section is a hexagon . when this volume is removed from a sphere to form a dimple , the intersecting surface is not planar , but rather resembles a hexagon having curved edges . fig3 shows the geometry defined by the intersection of two cylinders of the same diameter and is a symmetric bi - cylinder 8 with the circumscribed square prism shown in phantom . bi - cylinders are formed from two cylinders oriented 90 □ apart with a common axis of rotation central to the dimple volume . the configuration of the two - dimensional cross - sections are not squares . when this volume is removed from a sphere to form a dimple , the intersecting surface is not planar , but rather resembles a square having curved edges . fig4 shows the geometry defined by the intersection of three eccentric cylinders , i . e . a tri - semicylinder 10 with a triangular circumscribed prism shown in phantom . tri - semicylinders are formed from three cylinders oriented 120 □ apart with a common axis of rotation that is eccentric from the geometric center of the dimple volume . the configuration of the two - dimensional cross - sections is a triangle . when this volume is removed from a sphere to form a dimple , the intersecting surface is not planar , but rather resembles a triangle having curved edges . quad - cylinders ( not shown ) are formed from four cylinders oriented 45 □ apart with a common axis of rotation central to the dimple volume . the configuration of the two - dimensional cross - sections is an octagon . when this volume is removed from a sphere to form a dimple , the intersecting surface is not planar , but rather resembles an octagon having curved edges . in fig5 - 7 , there are shown dual radius cylinders used to form a further geometry for a further dimple configuration . a first cylinder 12 ( fig5 ) has a first radius r 12 which is used to define the bottom portion 14 of a dimple 16 in the surface of a golf ball 18 shown in fig7 . that is , the bottom portion 14 of the dimple 16 has a radius r 12 . second 20 and third 22 cylinders each have radii r 20 and r 22 which are significantly less than the radius r 12 of the first cylinder . in the preferred example shown , the radii r 20 and r 22 are equal . however , they may be different so long as they both are less than the radius r 12 . the second and third cylinders are arranged at an outer edge of the first cylinder as shown in fig5 , with the axes of all of the cylinders being parallel . the surfaces of second 20 and third 22 cylinders intersect the golf ball surface and thus define dimple bottom portions 24 and 26 , respectively . the bottom portion 24 has a radius r 20 from the second cylinder 20 and the bottom portion 26 has a radius r 22 from the third cylinder 22 . as shown in fig6 , it is preferred that the second and third cylinders overlap so that all three cylinders intersect and are tangent at the intersection . the intersection of the surfaces of the cylinders with the golf ball surface define the geometric configuration of the dimple bottom surface . the degree of overlap of the second and third cylinders will define the width of the dimple . stated another way , the golf ball 18 has x , y , and z axes and is centered at ( 0 , 0 , 0 ). the first cylinder 12 that forms the bottom of the dimple has its radius parallel with the z - axis of the ball and is centered at ( 0 , ye , 0 ). the first cylinder is sliced parallel with the yz plane at x = xa , with the central portion of the cylinder retained . the cylinder is then sliced parallel with the yz plane at x =− xa and the central portion is retained . next , the edge cylinders , i . e . the second 20 and third 22 cylinders are created . these cylinders have their radii centered at ( xc , yc ) and (− xc , yc ), respectively . the surface of the three solids defined by the joinder of the three cylinders defines the geometry of the dimple . this geometry can be used to create a dimple volume removal tool which is used to create a ball geometry for forming the dimples during molding of the cover layer of the golf ball . where the radii of the second and third cylinders are equal , the dimple defined by the intersecting cylindrical surfaces is referred to as a dual radius cylinder dimple . the first cylinder 12 has a first radius and the second and third cylinders 20 , 22 have a second radius . fig8 is a bottom view of a dual radius cylinder 28 including a large diameter cylinder portion 30 and two small diameter cylinder portions 32 , 34 , small cylinder portions having equal radii . as discussed above with reference to fig5 - 7 , the small diameter cylinder portions define the edge of a dimple the large diameter cylinder portion defines the bottom of a dimple . thus , the large diameter cylinder portion may be referred to as the bottom cylinder and the small diameter cylinder portions may be referred to as the edge cylinders . fig9 is a bottom view of a dual radius cylinder 36 including bottom cylinder 38 and edge cylinders 40 , 42 , and fig1 is a bottom view of a dual radius cylinder 44 including bottom cylinder 46 and edge cylinders 48 , 50 . the dual radius cylinders 36 and 44 are similar to the dual radius cylinder 28 . fig1 - 13 are side views of the dual radius cylinders 28 , 36 , and 44 of fig8 - 10 , respectively . fig1 shows the orientation of the dual radius cylinders 28 , 36 , and 44 prior to intersection and fig1 is a detailed bottom view of the geometry defined by the intersection of the surfaces of the dual radius cylinders . in fig1 , all volumes of the dual radius cylinders which do not intersect have been removed to define the geometry as shown . a perspective view of the intersection geometry of fig1 is shown in fig1 . it represents the volume of a dimple formed using the geometry . the portions 30 , 38 and 46 are formed by the bottom cylindrical surface of the dual radius cylinders and define the bottom surface of the dimple and the portions 32 , 34 , 40 , 42 , 48 , and 50 are formed by the edge cylindrical surfaces of the dual radius cylinders and define the edge surfaces of the dimple . fig1 is a perspective view of a dual radius penta - semicylinder dimple . fig1 a shows a golf ball surface 52 having dimples 54 defined by a symmetric tri - cylinder as shown in fig1 formed of dual radius cylinders as shown in fig1 . the upper portion of the tri - cylinder has six surfaces , two each of surfaces 30 , 38 , and 46 . each dimple 54 in the ball of fig1 a also has six surfaces 54 a - f corresponding to the upper surfaces of the tri - cylinder , respectively , as shown in fig1 b . the mid - portion of the tri - cylinder has another six surfaces 32 , 34 , 40 , 42 , 48 , and 50 which form the surfaces 54 g - l in the dimple 54 in fig1 b . the dimples can be sized and arranged on the ball surface in a desired pattern to maximize dimple coverage on the ball surface . the size and depth of the dimples is defined by the radii of the cylinders being used to create the geometries . a common design practice of placing dimples onto a golf ball is to begin at either the equator and work toward the pole , begin at the pole and work toward the equator , or begin at both the pole and equator and work toward the other simultaneously . it is also common that the preferred dimple sizes may not maximize surface area coverage . in this case , a variation to the n - cylinder ( bi , tri , quad , penta etc .) may be employed which in effect stretches the dimple in at least one direction , similar to the way in which a circular dimple would be stretched into an ellipse . such stretching could also result in a non - symmetric dimple . this is done to maximize surface area coverage and to create a cosmetically attractive layout . the dimple volumes can be combined to form dimple patterns with increased dimple coverage on the surface of a golf ball . by adjusting the cylindrical radius to be somewhat similar in value to the spherical radius that forms traditional spherical dimples , these new dimple shapes have edge angles , volumes , depths , and chordal diameters similar to traditional spherical dimples . individual dimple volumes can be tuned to match volume ratios that work for traditional spherical dimple patterns . the pair of smaller tangential cylinders allows the dimple volume and dimple edge angle to be adjusted independently . a golf ball 56 including dimples formed in accordance with a preferred embodiment of the invention is shown in fig1 . the golf ball includes 12 dual radius penta - semicylinder dimples 58 , 50 symmetric dual radius tri - cylinder dimples 60 , and 260 non - symmetric dual radius tri - cylinder dimples 62 . the pattern is repeated five times across the surface of the golf ball ( i . e . five - fold symmetry ) and provides 90 . 3 % dimple surface coverage . in lieu of intersecting cylinders , intersecting surfaces may also be used to define the geometry used to create dimple configurations in accordance with the invention . in fig2 - 23 , three planar surfaces intersect to form a tetrahedral volume . the top of the tetrahedron can be used to form the dimple geometry . the volume of fig2 is a full tetrahedron 64 . the cross - section of the tetrahedron taken along line 24 - 24 produces the dimple cross - sectional configuration shown in fig2 . the volume of fig2 is a truncated tetrahedron 66 . the top of the tetrahedron is truncated by a fourth planar surface which is parallel to the plane of the bottom of the tetrahedron . the cross - section of the tetrahedron 66 taken along line 25 - 25 produces the dimple cross - sectional configuration shown in fig2 . the volume of fig2 is a truncated tetrahedron 68 . the top of the tetrahedron is truncated by a fourth convex surface . the cross - section of the tetrahedron 68 taken along line 26 - 26 produces the dimple cross - sectional configuration shown in fig2 . the volume of fig2 is a truncated tetrahedron 70 . the top of the tetrahedron is truncated by a fourth concave surface . the cross - section of the tetrahedron 70 taken along line 27 - 27 produces the dimple cross - sectional configuration shown in fig2 . fig2 - 31 are similar to fig2 - 23 except that the tetrahedral volumes are defined by curved rather than planar surfaces . the curves may be portions of a sphere or cylinder or other curved geometric shape . the truncations in fig2 - 31 are formed by planar , concave , and convex surfaces , respectively , in the same manner as the truncations in fig2 - 23 . the dimple configurations resulting from cross - sections taken along lines 32 - 32 , 33 - 33 , 34 - 34 , and 35 - 35 are shown in fig3 , 33 , 34 , and 35 , respectively . in fig3 is shown a golf ball containing triangular dimples 72 with planar sides . the bottom surfaces of the dimples are formed by a sphere concentric with the golf ball surface but having a slightly smaller diameter than the golf ball . where the edges of the dimples meet , small fillet radii are provided to round off the transition between adjacent dimples . such a dimple pattern provides 93 . 86 % coverage of the golf ball surface where the dimple depth is 0 . 006 inches , the ball radius is 1 . 693 inches , the edge angle is 15 . 25 □, and the total volume ratio is 1 . 45 %. from the foregoing it is believed that those skilled in the pertinent art will recognize the meritorious advancement of this invention and will readily understand that while the present invention has been described in association with a preferred embodiment thereof , and other embodiments illustrated in the accompanying drawings , numerous changes , modifications and substitutions of equivalents may be made therein without departing from the spirit and scope of this invention which is intended to be unlimited by the foregoing except as may appear in the following appended claims . therefore , the embodiments of the invention in which an exclusive property or privilege is claimed are defined in the following appended claims .
a golf ball with a dimple pattern designed to maximize flight characteristics employs dimples which are created by joining two or more intersecting surfaces . the invention provides for single radius or dual radius dimples , preferably including smaller radius cylinders tangentially arranged along the side of the larger cylinders . the intersection of the cylinders forms tri - cylinders , tri - semicylinders , bi - cylinders , quad - semicylinders , penta - semicylinders , or more generally n - cylinders depending upon the number of intersecting cylinders . the golf ball includes a plurality of single or dual radius dimples created by intersecting n - cylinders to create maximum turbulence on the ball during flight .