Waterman Polyhedra

Root: 25 Radius: sqrt(50) Spheres: 767 Vertices: 132 Faces: 134 Edges: 264 Area: 593.99 Volume: 1332 0025.off p0025.pov s0025.pov
Root: 26 Radius: sqrt(52) Spheres: 791 Vertices: 96 Faces: 62 Edges: 156 Area: 608.485 Volume: 1364 0026.off p0026.pov s0026.pov
Root: 27 Radius: sqrt(54) Spheres: 887 Vertices: 120 Faces: 122 Edges: 240 Area: 654.027 Volume: 1540 0027.off p0027.pov s0027.pov
Root: 28 Radius: sqrt(56) Spheres: 935 Vertices: 96 Faces: 74 Edges: 168 Area: 666.437 Volume: 1572 0028.off p0028.pov s0028.pov
Root: 29 Radius: sqrt(58) Spheres: 959 Vertices: 72 Faces: 50 Edges: 120 Area: 676.921 Volume: 1596 0029.off p0029.pov s0029.pov
Root: 30 Radius: sqrt(60) Spheres: 959 Vertices: 72 Faces: 50 Edges: 120 Area: 676.921 Volume: 1596 0030.off p0030.pov s0030.pov
Root: 31 Radius: sqrt(62) Spheres: 1055 Vertices: 96 Faces: 50 Edges: 144 Area: 731.492 Volume: 1740 0031.off p0031.pov s0031.pov
Root: 32 Radius: sqrt(64) Spheres: 1061 Vertices: 102 Faces: 92 Edges: 192 Area: 741.635 Volume: 1808 0032.off p0032.pov s0032.pov
Root: 33 Radius: sqrt(66) Spheres: 1157 Vertices: 96 Faces: 122 Edges: 216 Area: 796.011 Volume: 2074 2/3 0033.off p0033.pov s0033.pov
Root: 34 Radius: sqrt(68) Spheres: 1205 Vertices: 96 Faces: 98 Edges: 192 Area: 811.132 Volume: 2122 2/3 0034.off p0034.pov s0034.pov
Root: 35 Radius: sqrt(70) Spheres: 1253 Vertices: 120 Faces: 74 Edges: 192 Area: 827.315 Volume: 2170 2/3 0035.off p0035.pov s0035.pov
Root: 36 Radius: sqrt(72) Spheres: 1289 Vertices: 84 Faces: 134 Edges: 216 Area: 854.583 Volume: 2306 2/3 0036.off p0036.pov s0036.pov
Root: 37 Radius: sqrt(74) Spheres: 1409 Vertices: 120 Faces: 134 Edges: 252 Area: 897.004 Volume: 2466 2/3 0037.off p0037.pov s0037.pov
Root: 38 Radius: sqrt(76) Spheres: 1433 Vertices: 144 Faces: 122 Edges: 264 Area: 907.692 Volume: 2506 2/3 0038.off p0038.pov s0038.pov
Root: 39 Radius: sqrt(78) Spheres: 1481 Vertices: 96 Faces: 74 Edges: 168 Area: 920.102 Volume: 2538 2/3 0039.off p0039.pov s0039.pov
Root: 40 Radius: sqrt(80) Spheres: 1505 Vertices: 72 Faces: 50 Edges: 120 Area: 930.587 Volume: 2562 2/3 0040.off p0040.pov s0040.pov
Root: 41 Radius: sqrt(82) Spheres: 1553 Vertices: 120 Faces: 146 Edges: 264 Area: 967.629 Volume: 2742 2/3 0041.off p0041.pov s0041.pov
Root: 42 Radius: sqrt(84) Spheres: 1601 Vertices: 72 Faces: 74 Edges: 144 Area: 982.646 Volume: 2774 2/3 0042.off p0042.pov s0042.pov
Root: 43 Radius: sqrt(86) Spheres: 1721 Vertices: 168 Faces: 170 Edges: 336 Area: 1046.49 Volume: 3137 1/3 0043.off p0043.pov s0043.pov
Root: 44 Radius: sqrt(88) Spheres: 1745 Vertices: 168 Faces: 170 Edges: 336 Area: 1054.1 Volume: 3169 1/3 0044.off p0044.pov s0044.pov
Root: 45 Radius: sqrt(90) Spheres: 1865 Vertices: 120 Faces: 98 Edges: 216 Area: 1092.68 Volume: 3321 1/3 0045.off p0045.pov s0045.pov
Root: 46 Radius: sqrt(92) Spheres: 1865 Vertices: 120 Faces: 98 Edges: 216 Area: 1092.68 Volume: 3321 1/3 0046.off p0046.pov s0046.pov
Root: 47 Radius: sqrt(94) Spheres: 1961 Vertices: 144 Faces: 122 Edges: 264 Area: 1132.14 Volume: 3497 1/3 0047.off p0047.pov s0047.pov
Root: 48 Radius: sqrt(96) Spheres: 1985 Vertices: 168 Faces: 122 Edges: 288 Area: 1141.13 Volume: 3529 1/3 0048.off p0048.pov s0048.pov
Root: 49 Radius: sqrt(98) Spheres: 2093 Vertices: 108 Faces: 134 Edges: 240 Area: 1182.64 Volume: 3713 1/3 0049.off p0049.pov s0049.pov
Root: 50 Radius: sqrt(100) Spheres: 2123 Vertices: 126 Faces: 176 Edges: 300 Area: 1198.54 Volume: 3829 1/3 0050.off p0050.pov s0050.pov
It's obvious that as the root increases then the polyhedra approaches a sphere. For example, root = 500 and 2000 are shown below.
Root: 500 Radius: sqrt(1000) Spheres: 66427 Vertices: 720 Faces: 698 Edges: 1416 Area: 12452.128 Volume: 130076
Root: 2000 Radius: sqrt(4000) Spheres: 529747 Vertices: 2016 Faces: 1994 Edges: 4008 Area: 50055.358 Volume: 1050876