Snub dodecahedron

Rhombitruncated cuboctahedron (8), Truncated dodecahedron (9), Truncated icosahedron (10), Rhombicosidodecahedron (11), Snub dodecahedron (12), Rhombitruncated icosidodecahedron (13) (see also Table 9.2). 

In addition to the Platonic solids, there exists a family of 13 convex uniform polyhedra known as the Archimedean solids. Each member of this family is made up of at least two different regular polygons and may be derived from at least one Platonic solid through either truncation or twisting of faces (Figure 3, Table 2). In the case of the latter, two chiral members, the snub cube and the snub dodecahedron, are realized. The remaining Archimedean solids are achiral. 

Figure 1. Therefore, in the search for the snub dodecahedron, utilizing calix[5]arene pentacarboxylic acid molecules as the pentagons and water as the triangles, the ratio of water to calix[5]pentacarboxylic acid cannot be higher than 60 12 (see Table 2). However, the ratio could (and probably will) be lower than 60 12.

Figure 2.24 Identification of one of two chiral 60-vertex cages, which correspond to the regular orbit of I symmetry and reduction of this regular orhit to find the lower structure orbits of the group. The set of five vertices about the topmost pole of a C5 axis of the regular orbit of I are coloured black in the elliptical projection and the perspective drawing of the snub dodecahedron. The other structural orbits of the I group follow by the usual sequence of contractions of the local sets of 5, 3 and 2 onto the poles of the rotational axes.

Figure 11. The 13 Archimedean solids, in order of increasing number of vertices. Truncated tetrahedron (1), cuboctahedron (2), truncated cube (3), truncated octahedron (4), rhombicuboctahedron (5), snub cube (6), icosidodecahedron (7), rhombi-truncated cuboctahedron (8), truncated dodecahedron (9), truncated icosahedron (10), rhombicosidodecahedron (11), snub dodecahedron (12), rhombitruncated icosidodecahedron (13) (see also Table 2).

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