Uniform Compounds of Uniform Polyhedra

Contents

Introduction

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 List

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

References

J. Skilling: "Uniform Compounds of Uniform Polyhedra," Mathematical Proceedings of the Cambridge Philosophical Society, Vol. 79, pp. 447-457, 1976.

Links

Last Updated

2008-03-03, 21:22