# Polyhedra Coordinates

Here are the 62 (x, y, z) coordinates for the 120 Polyhedron.

Recall that the 120 Polyhedron's vertices are also the vertices for:

• 10 Tetrahedra
• 5 Cubes
• 5 Octahedra
• 5 rhombic Dodecahedra
• 1 Icosahedron
• 1 regular Dodecahedron
• 1 rhombic Triacontahedron
• many jitterbugs
and, of course, the 120 Polyhedron itself.

These coordinates are given in terms of the Golden Mean (a.k.a. Golden Ratio) which is here symbolized by the letter "p".

"p^2" and "p^3" are the 2nd and 3rd powers of the Golden Mean.

Also below, I give the vertex, edge and face maps for each of the polyhedra mentioned above.

With this information, it is easy to program a computer (CAD system) to display, manipulate and obtain numeric information about these polyhedra.

## Coordinates

 Vertex Type X Y Z 1 A 0 0 2p^2 2 B p^2 0 p^3 3 A p p^2 p^3 4 C 0 p p^3 5 A -p p^2 p^3 6 B -p^2 0 p^3 7 A -p -p^2 p^3 8 C 0 -p p^3 9 A p -p^2 p^3 10 A p^3 p p^2 11 C p^2 p^2 p^2 12 B 0 p^3 p^2 13 C -p^2 p^2 p^2 14 A -p^3 p p^2 15 A -p^3 -p p^2 16 C -p^2 -p^2 p^2 17 B 0 -p^3 p^2 18 C p^2 -p^2 p^2 19 A p^3 -p p^2 20 C p^3 0 p 21 A p^2 p^3 p 22 A -p^2 p^3 p 23 C -p^3 0 p 24 A -p^2 -p^3 p 25 A p^2 -p^3 p
 Vertex Type X Y Z 26 A 2p^2 0 0 27 B p^3 p^2 0 28 C p p^3 0 29 A 0 2p^2 0 30 C -p p^3 0 31 B -p^3 p^2 0 32 A -2p^2 0 0 33 B -p^3 -p^2 0 34 C -p -p^3 0 35 A 0 -2p^2 0 36 C p -p^3 0 37 B p^3 -p^2 0
 Vertex Type X Y Z 38 C p^3 0 -p 39 A p^2 p^3 -p 40 A -p^2 p^3 -p 41 C -p^3 0 -p 42 A -p^2 -p^3 -p 43 A p^2 -p^3 -p 44 A p^3 p -p^2 45 C p^2 p^2 -p^2 46 B 0 p^3 -p^2 47 C -p^2 p^2 -p^2 48 A -p^3 p -p^2 49 A -p^3 -p -p^2 50 C -p^2 -p^2 -p^2 51 B 0 -p^3 -p^2 52 C p^2 -p^2 -p^2 53 A p^3 -p -p^2 54 B p^2 0 -p^3 55 A p p^2 -p^3 56 C 0 p -p^3 57 A -p p^2 -p^3 58 B -p^2 0 -p^3 59 A -p -p^2 -p^3 60 C 0 -p -p^3 61 A p -p^2 -p^3 62 A 0 0 -2p^2

## 10 Tetrahedra

### Tetrahedron 1

 Vertices { 4, 34, 38, 47} Edge Map { 4, 34}, { 4, 38}, { 4, 47}, {34, 38}, {34, 47}, {38, 47} Face Map { 4, 34, 47}, { 4, 38, 34}, { 4, 47, 38}, {34, 38, 47}

### Tetrahedron 2

 Vertices {18, 23, 28, 60} Edge Map {18, 23}, {18, 28}, {18, 60}, {23, 28}, {23, 60}, {28, 60} Face Map {18, 23, 28}, {18, 23, 60}, {18, 28, 60}, {23, 28, 60}

### Tetrahedron 3

 Vertices { 4, 36, 41, 45} Edge Map { 4, 36}, { 4, 41}, { 4, 45}, {36, 41}, {36, 45}, {41, 45} Face Map { 4, 41, 36}, { 4, 36, 45}, { 4, 45, 41}, {36, 41, 45}

### Tetrahedron 4

 Vertices {16, 20, 30, 60} Edge Map {16, 20}, {16, 30}, {16, 60}, {20, 30}, {20, 60}, {30, 60} Face Map {16, 20, 30}, {16, 20, 60}, {16, 30, 60}, {20, 30, 60}

### Tetrahedron 5

 Vertices { 8, 28, 41, 52} Edge Map { 8, 28}, { 8, 41}, { 8, 52}, {28, 41}, {28, 52}, {41, 52} Face Map { 8, 28, 41}, { 8, 28, 52}, { 8, 41, 52}, {28, 41, 52}

### Tetrahedron 6

 Vertices {13, 20, 34, 56} Edge Map {13, 20}, {13, 34}, {13, 56}, {20, 34}, {20, 56}, {34, 56} Face Map {13, 20, 34}, {13, 20, 56}, {13, 34, 56}, {20, 34, 56}

### Tetrahedron 7

 Vertices { 8, 30, 38, 50} Edge Map { 8, 30}, { 8, 38}, { 8, 50}, {30, 38}, {30, 50}, {38, 50} Face Map { 8, 30, 38}, { 8, 30, 50}, { 8, 38, 50}, {30, 38, 50}

### Tetrahedron 8

 Vertices {11, 23, 36, 56} Edge Map {11, 23}, {11, 36}, {11, 56}, {23, 36}, {23, 56}, {36, 56} Face Map {11, 23, 36}, {11, 23, 56}, {11, 36, 56}, {23, 36, 56}

### Tetrahedron 9

 Vertices {11, 16, 47, 52} Edge Map {11, 16}, {11, 47}, {11, 52}, {16, 47}, {16, 52}, {47, 52} Face Map {47, 16, 11}, {52, 47, 11}, {16, 52, 11}, {47, 52, 16}

### Tetrahedron 10

 Vertices {13, 18, 45, 50} Edge Map {13, 18}, {13, 45}, {13, 50}, {18, 45}, {18, 50}, {45, 50} Face Map {13, 18, 45}, {13, 18, 50}, {13, 45, 50}, {18, 45, 50}

## 5 Cubes

Note: For the face maps, the Cube's square faces are divided into triangles. It is a common practice in graphics applications to divide polygons into triangles.

### Cube 1

 Vertices { 4, 18, 23, 28, 34, 38, 47, 60} Edge Map { 4, 18}, {18, 38}, {38, 28}, {28, 4}, { 4, 23}, {18, 34}, {28, 47}, {38, 60}, {23, 34}, {34, 60}, {60, 47}, {47, 23} Face Map {( 4, 18, 38), (38, 28, 4)}, {( 4, 23, 18), (18, 23, 34)}, {( 4, 28, 47), ( 4, 47, 23)}, {(28, 38, 60), (28, 60, 47)}, {(23, 47, 34), (47, 60, 34)}, {(38, 18, 60), (18, 34, 60)}

### Cube 2

 Vertices { 4, 16, 20, 30, 36, 41, 45, 60} Edge Map { 4, 16}, {16, 36}, {36, 20}, {20, 4}, { 4, 30}, {16, 41}, {20, 45}, {36, 60}, {30, 41}, {41, 60}, {60, 45}, {45, 30} Face Map {( 4, 16, 20), (16, 36, 20)}, {( 4, 20, 45), ( 4, 45, 30)}, {( 4, 30, 41), ( 4, 41, 16)}, {(45, 41, 30), (45, 60, 41)}, {(20, 36, 60), (20, 60, 45)}, {(36, 16, 41), (36, 41, 60}}

### Cube 3

 Vertices { 8, 13, 20, 28, 34, 41, 52, 56} Edge Map { 8, 13}, {13, 28}, {28, 20}, {20, 8}, { 8, 34}, {13, 41}, {28, 56}, {20, 52}, {34, 41}, {41, 56}, {56, 52}, {52, 34} Face Map {( 8, 13, 20), (13, 28, 20)}, {( 8, 20, 52), ( 8, 52, 34)}, {( 8, 34, 41), ( 8, 41, 13)}, {(20, 28, 56), (20, 56, 52)}, {(52, 56, 41), (52, 41, 34)}, {(28, 13, 41), (28, 41, 56)}

### Cube 4

 Vertices { 8, 11, 23, 30, 36, 38, 50, 56} Edge Map { 8, 11}, {11, 30}, {30, 23}, {23, 8}, { 8, 36}, {11, 38}, {23, 50}, {30, 56}, {36, 38}, {38, 56}, {56, 50}, {50, 36} Face Map {( 8, 11, 23), (11, 30, 23)}, {( 8, 23, 50), ( 8, 50, 36)}, {( 8, 36, 38), ( 8, 38, 11)}, {(23, 30, 56), (23, 56, 50)}, {(50, 56, 38), (50, 38, 36)}, {(30, 11, 56), (11, 38, 56)}

### Cube 5

 Vertices {11, 13, 16, 18, 45, 47, 50, 52} Edge Map {11, 13}, {13, 16}, {16, 18}, {18, 11}, {11, 45}, {13, 47}, {16, 50}, {18, 52}, {45, 47}, {47, 50}, {50, 52}, {52, 45} Face Map {(11, 13, 16), (11, 16, 18)}, {(11, 45, 47), (11, 47, 13)}, {(13, 47, 50), (13, 50, 16)}, {(16, 50, 52), (16, 52, 18)}, {(18, 52, 45), (18, 45, 11)}, {(45, 50, 52), (45, 47, 50)}

## 5 Octahedra

### Octahedron 1

 Vertices { 7, 10, 22, 43, 49, 55} Edge Map { 7, 10}, { 7, 22}, { 7, 43}, { 7, 49}, {10, 22}, {10, 43}, {22, 49}, {43, 49}, {10, 55}, {22, 55}, {43, 55}, {49, 55} Face Map { 7, 10, 43}, { 7, 22, 10}, { 7, 43, 49}, { 7, 49, 22}, {55, 10, 43}, {55, 22, 10}, {55, 43, 49}, {55, 49, 22}

### Octahedron 2

 Vertices { 9, 14, 21, 42, 53, 57} Edge Map { 9, 14}, { 9, 21}, { 9, 42}, { 9, 53}, {14, 21}, {14, 42}, {21, 53}, {42, 53}, {14, 57}, {21, 57}, {42, 57}, {53, 57} Face Map { 9, 14, 21}, { 9, 21, 53}, { 9, 42, 14}, { 9, 53, 42}, {57, 14, 21}, {57, 21, 53}, {57, 42, 14}, {57, 53, 42}

### Octahedron 3

 Vertices { 3, 15, 25, 40, 44, 59} Edge Map { 3, 15}, { 3, 25}, { 3, 40}, { 3, 44}, {15, 25}, {15, 40}, {40, 44}, {25, 44}, {25, 59}, {15, 59}, {40, 59}, {44, 59} Face Map { 3, 15, 25}, { 3, 25, 44}, { 3, 40, 15}, { 3, 44, 40}, {59, 25, 15}, {59, 15, 40}, {59, 40, 44}, {59, 44, 25}

### Octahedron 4

 Vertices { 5, 19, 24, 39, 48, 61} Edge Map { 5, 19}, { 5, 24}, { 5, 39}, { 5, 48}, {19, 24}, {19, 39}, {24, 48}, {39, 48}, {19, 61}, {24, 61}, {39, 61}, {48, 61} Face Map { 5, 19, 39}, { 5, 24, 19}, { 5, 39, 48}, { 5, 48, 24}, {61, 19, 39}, {61, 24, 19}, {61, 39, 48}, {61, 48, 24}

### Octahedron 5

 Vertices { 1, 26, 29, 32, 35, 62} Edge Map { 1, 26}, { 1, 29}, { 1, 32}, { 1, 35}, {26, 29}, {29, 32}, {32, 35}, {35, 26}, {62, 26}, {62, 29}, {62, 32}, {62, 35} Face Map { 1, 26, 29}, { 1, 29, 32}, { 1, 32, 35}, { 1, 35, 26}, {62, 29, 26}, {62, 32, 29}, {62, 35, 32}, {62, 26, 35}

## 5 Rhombic Dodecahedra

Note: For the face maps, the rhombic Dodecahedron's diamond faces are divided into triangles. It is a common practice in graphics applications to divide polygons into triangles.

### Rhombic Dodecahedron 1

 Vertices { 4, 7, 10, 18, 22, 23, 28, 34, 38, 43, 47, 49, 55, 60}, Edge Map { 7, 4}, { 7, 18}, { 7, 23}, { 7, 34}, {10, 4}, {10, 18}, {10, 28}, {10, 38}, {22, 4}, {22, 23}, {22, 28}, {22, 47}, {43, 18}, {43, 34}, {43, 38}, {43, 60}, {49, 23}, {49, 34}, {49, 47}, {49, 60}, {55, 28}, {55, 38}, {55, 47}, {55, 60} Face Map {( 7, 4, 18), (10, 4, 18)}, {( 7, 18, 34), (43, 18, 34)}, {( 7, 34, 23), (49, 34, 23)}, {( 7, 4, 23), (22, 4, 23)}, {(22, 4, 28), (10, 4, 28)}, {(18, 10, 43), (38, 10, 43)}, {(34, 49, 43), (60, 49, 43)}, {(23, 49, 22), (47, 49, 22)}, {(55, 38, 60), (43, 38, 60)}, {(55, 60, 47), (49, 60, 47)}, {(55, 47, 28), (22, 47, 28)}, {(55, 28, 38), (10, 28, 38)}

### Rhombic Dodecahedron 2

 Vertices { 4, 9, 14, 16, 20, 21, 30, 36, 41, 42, 45, 53, 57, 60}, Edge Map { 9, 4}, { 9, 16}, { 9, 20}, { 9, 36}, {14, 4}, {14, 16}, {14, 30}, {14, 41}, {21, 4}, {21, 20}, {21, 30}, {21, 45}, {42, 16}, {42, 36}, {42, 41}, {42, 60}, {53, 20}, {53, 36}, {53, 45}, {53, 60}, {57, 30}, {57, 41}, {57, 45}, {57, 60} Face Map {( 9, 4, 16), (14, 4, 16)}, {( 9, 16, 36), (42, 16, 36)}, {( 9, 36, 20), (53, 36, 20)}, {( 9, 20, 4), (21, 20, 4)}, {(14, 4, 30), (21, 4, 30)}, {(16, 42, 14), (41, 42, 14)}, {(36, 42, 53), (60, 42, 53)}, {(20, 21, 53), (45, 21, 53)}, {(42, 41, 60), (57, 41, 60)}, {(53, 45, 60), (57, 45, 60)}, {(21, 30, 45), (57, 30, 45)}, {(14, 41, 30), (57, 41, 30)}

### Rhombic Dodecahedron 3

 Vertices { 3, 8, 13, 15, 20, 25, 28, 34, 40, 41, 44, 52, 56, 59}, Edge Map { 3, 8}, { 3, 13}, { 3, 20}, { 3, 28}, {15, 8}, {15, 13}, {15, 34}, {15, 41}, {25, 8}, {25, 20}, {25, 34}, {25, 52}, {40, 13}, {40, 28}, {40, 41}, {40, 56}, {44, 20}, {44, 28}, {44, 52}, {44, 56}, {59, 34}, {59, 41}, {59, 52}, {59, 56} Face Map {( 3, 8, 13), (15, 8, 13)}, {( 3, 13, 28), (40, 13, 28)}, {( 3, 28, 20), (44, 28, 20)}, {( 3, 20, 8), (25, 20, 8)}, {( 8, 25, 15), (34, 25, 15)}, {(13, 15, 40), (41, 15, 40)}, {(28, 44, 40), (56, 44, 40)}, {(20, 44, 25), (52, 44, 25)}, {(15, 41, 34), (59, 41, 34)}, {(40, 56, 41), (59, 56, 41)}, {(44, 56, 52), (59, 56, 52)}, {(25, 34, 52), (59, 34, 52)}

### Rhombic Dodecahedron 4

 Vertices { 5, 8, 11, 19, 23, 24, 30, 36, 38, 39, 48, 50, 56, 61}, Edge Map { 5, 8}, { 5, 11}, { 5, 23}, { 5, 30}, {19, 8}, {19, 11}, {19, 36}, {19, 38}, {24, 8}, {24, 23}, {24, 36}, {24, 50}, {39, 11}, {39, 30}, {39, 38}, {39, 56}, {48, 23}, {48, 30}, {48, 50}, {48, 56}, {61, 36}, {61, 38}, {61, 50}, {61, 56} Face Map {( 5, 8, 11), (19, 8, 11)}, {( 5, 11, 30), (39, 11, 30)}, {( 5, 30, 23), (48, 30, 23)}, {( 5, 23, 8), (24, 23, 8)}, {( 8, 19, 24), (36, 19, 24)}, {(11, 19, 39), (38, 19, 39)}, {(30, 39, 48), (56, 39, 48)}, {(23, 48, 24), (50, 48, 24)}, {(19, 38, 36), (61, 38, 36)}, {(39, 38, 56), (61, 38, 56)}, {(48, 50, 56), (61, 50, 56)}, {(24, 36, 50), (61, 36, 50)}

### Rhombic Dodecahedron 5

 Vertices { 1, 11, 13, 16, 18, 26, 29, 32, 35, 45, 47, 50, 52, 62}, Edge Map { 1, 11}, { 1, 13}, { 1, 16}, { 1, 18}, {26, 18}, {26, 11}, {26, 45}, {26, 52}, {29, 11}, {29, 13}, {29, 47}, {29, 45}, {32, 13}, {32, 16}, {32, 50}, {32, 47}, {35, 16}, {35, 18}, {35, 52}, {35, 50}, {62, 45}, {62, 47}, {62, 50}, {62, 52} Face Map {( 1, 11, 29), (29, 13, 1)}, {( 1, 13, 32), (32, 16, 1)}, {( 1, 16, 35), (35, 18, 1)}, {( 1, 18, 26), (26, 11, 1)}, {(26, 45, 29), (29, 11, 26)}, {(29, 47, 32), (32, 13, 29)}, {(32, 50, 35), (35, 16, 32)}, {(35, 52, 26), (26, 18, 35)}, {(62, 45, 26), (26, 52, 62)}, {(62, 47, 29), (29, 45, 62)}, {(62, 50, 32), (32, 47, 62)}, {(62, 52, 35), (35, 50, 62)}

## Regular Dodecahedron

Note: For the face maps, the Dodecahedron's pentagon faces are divided into triangles. It is a common practice in graphics applications to divide polygons into triangles.

 Vertices { 4, 8, 11, 13, 16, 18, 20, 23, 28, 30, 34, 36, 38, 41, 45, 47, 50, 52, 56, 60}, Edge Map { 4, 8}, { 4, 11}, { 4, 13}, { 8, 16}, { 8, 18}, {11, 20}, {11, 28}, {13, 30}, {13, 23}, {16, 23}, {16, 34}, {18, 36}, {18, 20}, {20, 38}, {23, 41}, {28, 30}, {28, 45}, {30, 47}, {34, 50}, {34, 36}, {36, 52}, {38, 45}, {38, 52}, {41, 47}, {41, 50}, {45, 56}, {47, 56}, {50, 60}, {52, 60}, {56, 60} Face Map {( 4, 8, 11), (11, 8, 18), (11, 18, 20)}, {( 4, 13, 23), ( 4, 23, 8), ( 8, 23, 16)}, {( 4, 11, 28), ( 4, 28, 30), ( 4, 30, 13)}, {( 8, 16, 34), ( 8, 34, 18), (18, 34, 36)}, {(11, 20, 28), (20, 45, 28), (20, 38, 45)}, {(13, 30, 23), (23, 30, 41), (41, 30, 47)}, {(16, 23, 34), (34, 23, 50), (50, 23, 41)}, {(18, 36, 52), (18, 52, 38), (18, 38, 20)}, {(28, 45, 56), (28, 56, 47), (28, 47, 30)}, {(34, 50, 60), (34, 60, 36), (36, 60, 52)}, {(38, 52, 60), (38, 60, 56), (38, 56, 45)}, {(41, 47, 56), (41, 56, 60), (41, 60, 50}

## Icosahedron

 Vertices { 2, 6, 12, 17, 27, 31, 33, 37, 46, 51, 54, 58} Edge Map { 2, 6}, { 2, 12}, { 2, 17}, { 2, 37}, { 2, 27}, { 6, 12}, { 6, 17}, { 6, 31}, { 6, 33}, {12, 27}, {12, 46}, {12, 31}, {17, 33}, {17, 51}, {17, 37}, {27, 37}, {27, 54}, {27, 46}, {31, 46}, {31, 58}, {31, 33}, {33, 58}, {33, 51}, {37, 51}, {37, 54}, {46, 54}, {46, 58}, {51, 54}, {51, 58}, {54, 58} Face Map { 2, 6, 17}, { 2, 12, 6}, { 2, 17, 37}, { 2, 37, 27}, { 2, 27, 12}, {37, 54, 27}, {27, 54, 46}, {27, 46, 12}, {12, 46, 31}, {12, 31, 6}, { 6, 31, 33}, { 6, 33, 17}, {17, 33, 51}, {17, 51, 37}, {37, 51, 54}, {58, 54, 51}, {58, 46, 54}, {58, 31, 46}, {58, 33, 31}, {58, 51, 33}

## Rhombic Triacontahedra

Note: For the face maps, the rhombic Triacontahedron's diamond faces are divided into triangles. It is a common practice in graphics applications to divide polygons into triangles.

### Rhombic Triacontahedron

 Vertices { 2, 4, 6, 8, 11, 12, 13, 16, 17, 18, 20, 23, 27, 28, 30, 31, 33, 34, 36, 37, 38, 41, 45, 46, 47, 50, 51, 52, 54, 56, 58, 60} Edge Map { 2, 4}, { 4, 6}, { 6, 8}, { 8, 2}, { 2, 11}, {11, 12}, { 4, 12}, {12, 13}, {13, 6}, { 6, 23}, { 6, 16}, {16, 17}, {17, 8}, {17, 18}, { 2, 18}, { 2, 20}, {20, 27}, {27, 28}, {12, 28}, {12, 30}, {13, 31}, {23, 31}, {23, 33}, {33, 16}, {18, 37}, {37, 20}, {11, 27}, {54, 56}, {56, 58}, {58, 60}, {60, 54}, {54, 45}, {45, 46}, {46, 56}, {58, 47}, {58, 41}, {58, 50}, {60, 51}, {52, 54}, {54, 38}, {38, 27}, {27, 45}, {46, 47}, {47, 31}, {31, 41}, {41, 33}, {33, 50}, {50, 51}, {51, 52}, {52, 37}, {37, 38}, {28, 46}, {30, 46}, {30, 31}, {17, 36}, {36, 51}, {51, 34}, {34, 17}, {36, 37}, {33, 34} Face Map {( 2, 4, 6), ( 6, 8, 2)}, {( 2, 11, 4), ( 4, 11, 12)}, {( 4, 12, 13), ( 4, 13, 6)}, {( 6, 16, 8), ( 8, 16, 17)}, {( 8, 17, 18), ( 8, 18, 2)}, {( 2, 18, 37), ( 2, 37, 20)}, {( 2, 20, 27), ( 2, 27, 11)}, {(11, 27, 28), (11, 28, 12)}, {( 6, 13, 31), ( 6, 31, 23)}, {( 6, 23, 33), ( 6, 33, 16)}, {(54, 60, 58), (58, 56, 54)}, {(54, 56, 45), (45, 56, 46)}, {(56, 58, 47), (47, 46, 56)}, {(47, 58, 41), (41, 31, 47)}, {(58, 50, 33), (33, 41, 58)}, {(58, 60, 51), (51, 50, 58)}, {(60, 54, 52), (52, 51, 60)}, {(54, 38, 37), (37, 52, 54)}, {(45, 27, 38), (38, 54, 45)}, {(20, 37, 38), (38, 27, 20)}, {(23, 31, 41), (41, 33, 23)}, {(12, 28, 46), (46, 30, 12)}, {(12, 30, 31), (31, 13, 12)}, {(31, 30, 46), (46, 47, 31)}, {(28, 27, 45), (45, 46, 28)}, {(17, 34, 51), (51, 36, 17)}, {(18, 17, 36), (36, 37, 18)}, {(37, 36, 51), (51, 52, 37)}, {(17, 16, 33), (33, 34, 17)}, {(34, 33, 50), (50, 51, 34)}

## 120 Polyhedron

 Vertices { 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62} Edge Map { 1, 2}, { 1, 4}, { 1, 6}, { 1, 8}, { 2, 3}, { 2, 4}, { 2, 8}, { 2, 9}, { 2, 10}, { 2, 11}, { 2, 18}, { 2, 19}, { 2, 20}, { 3, 4}, { 3, 11}, { 3, 12}, { 4, 5}, { 4, 6}, { 4, 12}, { 5, 6}, { 5, 12}, { 5, 13}, { 6, 7}, { 6, 8}, { 6, 13}, { 6, 14}, { 6, 15}, { 6, 16}, { 6, 23}, { 7, 8}, { 7, 16}, { 7, 17}, { 8, 9}, { 8, 17}, { 9, 17}, { 9, 18}, {10, 11}, {10, 20}, {10, 27}, {11, 12}, {11, 21}, {11, 27}, {12, 13}, {12, 21}, {12, 28}, {12, 29}, {12, 22}, {12, 30}, {13, 14}, {13, 22}, {13, 31}, {14, 23}, {14, 31}, {15, 16}, {15, 23}, {15, 33}, {16, 17}, {16, 24}, {16, 33}, {17, 18}, {17, 24}, {17, 25}, {17, 34}, {17, 35}, {17, 36}, {18, 19}, {18, 25}, {18, 37}, {19, 20}, {19, 37}, {20, 26}, {20, 27}, {20, 37}, {21, 27}, {21, 28}, {22, 30}, {22, 31}, {23, 31}, {23, 32}, {23, 33}, {24, 33}, {24, 34}, {25, 36}, {25, 37}, {26, 27}, {26, 37}, {26, 38}, {27, 28}, {27, 38}, {27, 39}, {27, 44}, {27, 45}, {28, 29}, {28, 39}, {28, 46}, {29, 30}, {29, 46}, {30, 31}, {30, 40}, {30, 46}, {31, 32}, {31, 40}, {31, 41}, {31, 47}, {31, 48}, {32, 33}, {32, 41}, {33, 34}, {33, 41}, {33, 42}, {33, 49}, {33, 50}, {34, 35}, {34, 42}, {34, 51}, {35, 36}, {35, 51}, {36, 37}, {36, 43}, {36, 51}, {37, 38}, {37, 43}, {37, 52}, {37, 53}, {38, 44}, {38, 53}, {38, 54}, {39, 45}, {39, 46}, {40, 46}, {40, 47}, {41, 48}, {41, 49}, {41, 58}, {42, 50}, {42, 51}, {43, 51}, {43, 52}, {44, 45}, {44, 54}, {45, 54}, {45, 55}, {45, 46}, {46, 47}, {46, 55}, {46, 56}, {46, 57}, {47, 48}, {47, 57}, {47, 58}, {48, 58}, {49, 50}, {49, 58}, {50, 51}, {50, 58}, {50, 59}, {51, 52}, {51, 59}, {51, 60}, {51, 61}, {52, 53}, {52, 61}, {52, 54}, {53, 54}, {54, 55}, {54, 56}, {54, 60}, {54, 61}, {54, 62}, {55, 56}, {56, 57}, {56, 58}, {56, 62}, {57, 58}, {58, 59}, {58, 60}, {58, 62}, {59, 60}, {60, 61}, {60, 62} Face Map { 1, 2, 4}, { 2, 3, 4}, { 2, 20, 10}, { 2, 10, 11}, { 2, 11, 3}, { 3, 11, 12}, { 3, 12, 4}, {20, 26, 27}, {20, 27, 10}, {10, 27, 11}, {11, 27, 21}, {11, 21, 12}, {21, 27, 28}, {12, 21, 28}, {12, 28, 29}, { 1, 4, 6}, { 4, 12, 5}, { 4, 5, 6}, { 5, 12, 13}, { 5, 13, 6}, { 6, 13, 14}, { 6, 14, 23}, {12, 29, 30}, {12, 30, 22}, {12, 22, 13}, {13, 22, 31}, {22, 30, 31}, {13, 31, 14}, {14, 31, 23}, {23, 31, 32}, { 1, 6, 8}, { 6, 23, 15}, { 6, 15, 16}, { 6, 16, 7}, { 6, 7, 8}, { 8, 7, 17}, { 7, 16, 17}, {23, 32, 33}, {15, 23, 33}, {16, 15, 33}, {24, 16, 33}, {34, 24, 33}, {17, 16, 24}, {17, 24, 34}, {17, 34, 35}, { 1, 8, 2}, { 8, 17, 9}, { 8, 9, 2}, { 9, 17, 18}, { 9, 18, 2}, { 2, 18, 19}, { 2, 19, 20}, {17, 35, 36}, {17, 36, 25}, {17, 25, 18}, {18, 25, 37}, {25, 36, 37}, {19, 18, 37}, {20, 19, 37}, {20, 37, 26}, {27, 26, 38}, {27, 38, 44}, {27, 44, 45}, {27, 45, 39}, {27, 39, 28}, {28, 39, 46}, {28, 46, 29}, {39, 45, 46}, {38, 54, 44}, {55, 45, 54}, {45, 44, 54}, {45, 55, 46}, {46, 55, 56}, {55, 54, 56}, {56, 54, 62}, {30, 29, 46}, {30, 46, 40}, {31, 30, 40}, {40, 46, 47}, {31, 40, 47}, {31, 47, 48}, {31, 48, 41}, {31, 41, 32}, {46, 56, 57}, {47, 46, 57}, {47, 57, 58}, {48, 47, 58}, {41, 48, 58}, {57, 56, 58}, {58, 56, 62}, {33, 32, 41}, {33, 41, 49}, {33, 49, 50}, {33, 50, 42}, {33, 42, 34}, {34, 42, 51}, {42, 50, 51}, {35, 34, 51}, {49, 41, 58}, {50, 49, 58}, {50, 58, 59}, {51, 50, 59}, {51, 59, 60}, {59, 58, 60}, {60, 58, 62}, {36, 35, 51}, {36, 51, 43}, {37, 36, 43}, {43, 51, 52}, {37, 43, 52}, {37, 52, 53}, {37, 53, 38}, {37, 38, 26}, {51, 60, 61}, {52, 51, 61}, {52, 61, 54}, {53, 52, 54}, {38, 53, 54}, {54, 61, 60}, {54, 60, 62}

Copyright November 2001, Robert W. Gray