Truncated icosidodecahedron

Fig. 9.9 The 13 Archimedean solids, in order of increasing number of vertices. Truncated tetrahedron (1), Cuboctahedron (2), Truncated cube (3), Truncated octahedron (4), Rhombicubocta-hedron (5), Snub cube (6), Icosidodecahedron (7),...

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

The complexity order of Archimedean solids in terms of the solid angle of their vertices is280 TT < CO < TC < TO < RCO < ID < TCO < TD < TCO < RID < TID. The two chiral Archimedean solids (snub octahedron, snub icosidodecahedron) were not considered. This order disagree with all four complexity given above, except in the case of the truncated tetrahedron which is predicted to be the least complex of all Archimedean solids. This discrepancy is perhaps due to different bases of the compared complexity orders the above orders being the result of 2D representation and the Balaban-Bonchev order of 3D structure of Archimedean solids. 

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