In [1] J. Skilling summarises all compounds of the uniform polyhedra that are themselves uniform. This page summarises this list and shows the compounds as VRML files.
| Skilling's Nr | Wythoff's symbol of Constituent | Symmetry of Compound | Number of Constituents | VRML Model(s) |
| 1 | 3 | 2 3
(tetrahedron) |
Td | 6 | dynamic
example |
| 2 | Oh | 12 | dynamic
example |
|
| 3 | Oh | 6 | static | |
| 4 | Oh | 2 | static | |
| 5 | I | 5 | static | |
| 6 | Ih | 10 | static | |
| 7 | 3 | 2 4
(cube) |
Oh | 6 | dynamic
example |
| 8 | Oh | 3 | static | |
| 9 | Ih | 5 | no model yet | |
| 10 | 4 | 2 3
(octahedron) |
Td | 4 | dynamic
example |
| 11 | Oh | 8 | dynamic
example |
|
| 12 | Oh | 4 | static | |
| 13 | Ih | 20 | no model yet | |
| 14 | Ih | 20 | no model yet | |
| 15 | Ih | 10 | no model yet | |
| 16 | Ih | 10 | no model yet | |
| 17 | Ih | 5 | no model yet | |
| 18 | 3/2 | 2 3
(tetrahemihexahedron) |
I | 5 | no model yet |
| 19 | I | 20 | no model yet | |
| 20 | 2n/m | 2
(n/m-gonal prism) |
Drn, h | 2r | no model yet |
| 21 | Drn, h | r | no model yet | |
| 22 | | 2 2 n/m (m odd)
(n/m-gonal antiprism) |
Drn, d (r odd)
Drn, h (r even) |
2r | no model yet |
| 23 | Drn, d (r odd)
Drn, h (r even) |
r | no model yet | |
| 24 | | 2 2 n/m (m even)
(n/m-gonal antiprism) |
Drn, h (r odd) | 2r | no model yet |
| 25 | Drn, h (r odd) | r | no model yet | |
| 26 | | 2 2 5
(pentagonal antiprism) |
Ih | 12 | dynamic
example |
| 27 | Ih | 6 | static | |
| 28 | | 2 2 5/3
(crossed pentagrammic antiprism) |
Ih | 12 | dynamic
example |
| 29 | Ih | 6 | static | |
| 30 | 2 3 | 2
(triangular prism) |
O | 4 | no model yet |
| 31 | Oh | 8 | no model yet | |
| 32 | I | 10 | no model yet | |
| 33 | Ih | 20 | no model yet | |
| 34 | 2 5 | 2
(pentagonal prism) |
I | 6 | no model yet |
| 35 | Ih | 6 | no model yet | |
| 36 | 2 5/2 | 2
(pentagrammic prism) |
I | 6 | no model yet |
| 37 | Ih | 6 | no model yet | |
| 38 | 2 6 | 2
(hexagonal prism) |
Oh | 4 | no model yet |
| 39 | Ih | 10 | no model yet | |
| 40 | 2 10 | 2
(decagocal prism) |
Ih | 6 | no model yet |
| 41 | 2 10/3 | 2
(decagrammic prism) |
Ih | 3 | no model yet |
| 42 | | 2 2 4
(square antiprism) |
O | 6 | no model yet |
| 43 | Oh | 3 | no model yet | |
| 44 | | 2 2 5/2
(pentagrammic antiprism) |
I | 6 | no model yet |
| 45 | Ih | 12 | no model yet | |
| 46 | 5 | 2 3
(icosahedron) |
Oh | 2 | no model yet |
| 47 | Ih | 5 | no model yet | |
| 48 | 5/2 | 2 5
(great dodecahedron) |
Oh | 2 | no model yet |
| 49 | Ih | 5 | no model yet | |
| 50 | 5 | 2 5/2
(small stellated dodecahedron) |
Oh | 2 | no model yet |
| 51 | Ih | 5 | no model yet | |
| 52 | 5/2 | 2 3
(great icosahedron) |
Oh | 2 | no model yet |
| 53 | Ih | 5 | no model yet | |
| 54 | 2 3 | 3
(truncated tetrahedron) |
Oh | 2 | no model yet |
| 55 | I | 5 | no model yet | |
| 56 | Ih | 10 | no model yet | |
| 57 | 2 3 | 4
(truncated cube) |
Ih | 5 | no model yet |
| 58 | 2 3 | 4/3
(stellated truncated cube) |
Ih | 5 | no model yet |
| 59 | 2 | 3 4
(cuboctahedron) |
Ih | 5 | no model yet |
| 60 | 4/34 | 3
(cubohemioctahedron) |
Ih | 5 | no model yet |
| 61 | 3/23 | 3
(octahemioctahedron) |
Ih | 5 | no model yet |
| 62 | 3 4 | 2
(small rhombicuboctahedron) |
Ih | 5 | no model yet |
| 63 | 2 4 34//22 |
(small rhombicube) |
Ih | 5 | no model yet |
| 64 | 3/24 | 4
(small cubicuboctahedron) |
Ih | 5 | no model yet |
| 65 | 3 4 | 4/3
(great cubicuboctahedron) |
Ih | 5 | no model yet |
| 66 | 2 4/334//22 |
(great rhombicube) |
Ih | 5 | no model yet |
| 67 | 3/24 | 2
(great rhombicuboctahedron) |
Ih | 5 | no model yet |
| 68 | | 2 3 4
(snub cube) |
Oh | 2 | no model yet |
| 69 | | 2 3 5
(snub dodecahedron) |
Ih | 2 | no model yet |
| 70 | | 2 3 5/2
(great snub icosidodecahedron) |
Ih | 2 | no model yet |
| 71 | | 2 3 5/3
(great inverted snub icosidodecahedron) |
Ih | 2 | no model yet |
| 72 | | 2 3/2 5/3
(great retrosnub icosidodecahedron) |
Ih | 2 | no model yet |
| 73 | | 2 5/2 5
(snub dodecadodecahedron) |
Ih | 2 | no model yet |
| 74 | | 2 5/3 5
(inverted snub dodecadodecahedron) |
Ih | 2 | no model yet |
| 75 | | 3 5/3 5
(snub icosidodecadodecahedron) |
Ih | 2 | no model yet |
2008-03-03, 21:22