Acronym | desided |
Name |
disnub icosidodecadodecahedron, compound of 2 sided |
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Circumradius |
sqrt[(2ρ-1)/(ρ-1)] = 1.126898
where ρ = (cbrt[9-sqrt(69)]+cbrt[9+sqrt(69)])/cbrt(18) = 1.324718 is the plastic number, the only real solution of x3-x-1=0 |
Vertex figure | [5/3,33,5,3] |
External links |
All, the icosahedral triangles, the pentagrams, and the pentagons, coincide by their face planes pairwise each. So either all are considered separately (type A); or triangle pairs are considered as (rotated) compounds while the other are considered separately (type B); or pentagram pairs are considered as (rotated) compounds while the other are considered separately (type C); or pentagon pairs are considered as (rotated) compounds while the other are considered separately (type D); or both, triangle pairs and pentagram pairs, are considered as compounds (type E); or both, triangle pairs and pentagon pairs, are considered as compounds (type F); or both, pentagram pairs and pentagon pairs, are considered as compounds (type G); or all are considered as compounds each (type H).
(Type A) 120 | 2 2 2 | 3 1 1 1 || 1 -----+-------------+--------------++-- 2 | 120 * * | 1 1 0 0 || 1 2 | * 120 * | 1 0 1 0 || 1 2 | * * 120 | 1 0 0 1 || 1 -----+-------------+--------------++-- 3 | 1 1 1 | 120 * * * || 1 3 | 3 0 0 | * 40 * * || 1 5 | 0 5 0 | * * 24 * || 1 5 | 0 0 5 | * * * 24 || 1 -----+-------------+--------------++-- ♦ 60 | 60 60 60 | 60 20 12 12 || 2
(Type B) 120 | 2 2 2 | 3 1 1 1 || 1 -----+-------------+--------------++-- 2 | 120 * * | 1 1 0 0 || 1 2 | * 120 * | 1 0 1 0 || 1 2 | * * 120 | 1 0 0 1 || 1 -----+-------------+--------------++-- 3 | 1 1 1 | 120 * * * || 1 6 | 6 0 0 | * 20 * * || 2 5 | 0 5 0 | * * 24 * || 1 5 | 0 0 5 | * * * 24 || 1 -----+-------------+--------------++-- ♦ 60 | 60 60 60 | 60 20 12 12 || 2
(Type C) 120 | 2 2 2 | 3 1 1 1 || 1 -----+-------------+--------------++-- 2 | 120 * * | 1 1 0 0 || 1 2 | * 120 * | 1 0 1 0 || 1 2 | * * 120 | 1 0 0 1 || 1 -----+-------------+--------------++-- 3 | 1 1 1 | 120 * * * || 1 3 | 3 0 0 | * 40 * * || 1 10 | 0 10 0 | * * 12 * || 2 5 | 0 0 5 | * * * 24 || 1 -----+-------------+--------------++-- ♦ 60 | 60 60 60 | 60 20 12 12 || 2
(Type D) 120 | 2 2 2 | 3 1 1 1 || 1 -----+-------------+--------------++-- 2 | 120 * * | 1 1 0 0 || 1 2 | * 120 * | 1 0 1 0 || 1 2 | * * 120 | 1 0 0 1 || 1 -----+-------------+--------------++-- 3 | 1 1 1 | 120 * * * || 1 3 | 3 0 0 | * 40 * * || 1 5 | 0 5 0 | * * 24 * || 1 10 | 0 0 10 | * * * 12 || 2 -----+-------------+--------------++-- ♦ 60 | 60 60 60 | 60 20 12 12 || 2
(Type E) 120 | 2 2 2 | 3 1 1 1 || 1 -----+-------------+--------------++-- 2 | 120 * * | 1 1 0 0 || 1 2 | * 120 * | 1 0 1 0 || 1 2 | * * 120 | 1 0 0 1 || 1 -----+-------------+--------------++-- 3 | 1 1 1 | 120 * * * || 1 6 | 6 0 0 | * 20 * * || 2 10 | 0 10 0 | * * 12 * || 2 5 | 0 0 5 | * * * 24 || 1 -----+-------------+--------------++-- ♦ 60 | 60 60 60 | 60 20 12 12 || 2
(Type F) 120 | 2 2 2 | 3 1 1 1 || 1 -----+-------------+--------------++-- 2 | 120 * * | 1 1 0 0 || 1 2 | * 120 * | 1 0 1 0 || 1 2 | * * 120 | 1 0 0 1 || 1 -----+-------------+--------------++-- 3 | 1 1 1 | 120 * * * || 1 6 | 6 0 0 | * 20 * * || 2 5 | 0 5 0 | * * 24 * || 1 10 | 0 0 10 | * * * 12 || 2 -----+-------------+--------------++-- ♦ 60 | 60 60 60 | 60 20 12 12 || 2
(Type G) 120 | 2 2 2 | 3 1 1 1 || 1 -----+-------------+--------------++-- 2 | 120 * * | 1 1 0 0 || 1 2 | * 120 * | 1 0 1 0 || 1 2 | * * 120 | 1 0 0 1 || 1 -----+-------------+--------------++-- 3 | 1 1 1 | 120 * * * || 1 3 | 3 0 0 | * 40 * * || 1 10 | 0 10 0 | * * 12 * || 2 10 | 0 0 10 | * * * 12 || 2 -----+-------------+--------------++-- ♦ 60 | 60 60 60 | 60 20 12 12 || 2
(Type H) 120 | 2 2 2 | 3 1 1 1 || 1 -----+-------------+--------------++-- 2 | 120 * * | 1 1 0 0 || 1 2 | * 120 * | 1 0 1 0 || 1 2 | * * 120 | 1 0 0 1 || 1 -----+-------------+--------------++-- 3 | 1 1 1 | 120 * * * || 1 6 | 6 0 0 | * 20 * * || 2 10 | 0 10 0 | * * 12 * || 2 10 | 0 0 10 | * * * 12 || 2 -----+-------------+--------------++-- ♦ 60 | 60 60 60 | 60 20 12 12 || 2
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