Archimedean solids truncated tetrahedron

Fig. 3 The 13 Archimedean solids Truncated tetrahedron (1), cuboctahedron (2), truncated cube (3). truncated octahedron (4). rhombicuboctahedron (5), snub cube (6). icosidodecahedron (7), rhombitruncated cuboctahedron (8), truncated dodecahedron (9). truncated icosahedron (10). rhombicosidodecahedron (11). snub dodecahedron (12), and rhombitruncated icosidodecahedron (13)...

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. 

Three or more molecules may assemble in the solid state to form a finite assembly with connecting forces propagated in 3D. The components of such an assembly will typically form a polyhedral shell. The shell may accommodate chemical species as guests. The polyhedron may be based on a prism or antiprism, as well as one of the five Platonic (e.g. cube, tetrahedron) or 13 Archimedean (e.g. truncated tetrahedron) solids.4... 

Fig. 5 Spherical hosts based on the Archimedean solids (a) metal-organic cage (truncated tetrahedron), (b) calix[4]resorcinarene spheroid (snub cube), and (c) buckminsterfullerene (truncated icosahedron). (View this art in color at www.dekker.com.)...

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