Polyhedra platonic

The three infinite families are represented as Nrs. 15, 44, and 61 in Table 9.1, by their smallest members. Nrs. 2, 18 of Table 9.1 can be seen as snub Prism3, snub Prism4. Now, Prism, APrism, snub Prisms are Platonic polyhedra. Prisms is given separately under Nr. 1 and not as a case in Nr. 15 of Prism, because it has a 4. 

Pig. 1. The scheme of Davisson for the analysis of substances in terms of the five Platonic polyhedra. Taken from Philosophia Pyrotechnica, part 3, Paris, 1642... 

There are five regular (Platonic) polyhedra with equivalent faces and equivalent vertices. Of these, the tetrahedron, octahedron, cube (hexahedron) and icosahedron are widely represented in cluster polyhedra. The structure descriptions in Table 1 illustrate the occurrence of regular polyhedra in cages and demonstrate the descriptive notation based on expanding concentric... 

The cage (8f), comprised of concentric Platonic polyhedra with virtual symmetry if the ligand... 

The most regular polyhedra, the Platonic polyhedra, are characterized by having all their faces formed by identical regular polygons, all their vertices equivalent, and all their edges equivalent. These polyhedra belong to the most symmetric point groups tetrahedral, octahedral, or icosahedral. 

Second to the Platonic polyhedra in terms of regularity is the family of the Archimedean solids, a set of 15 shapes whose faces are regular polygons and whose vertices are all equivalent. However, more than one type of faces is... 

FIGURE 1 Topology mapping of the Platonic polyhedra due to Wells. 

Thus in the diamond network, which corresponds to the Platonic (integer) topology of the Platonic polyhedra, one can readily trace the uniform 6-gon, puckered circuitry of the network connected together by all 4-con-nected, tetrahedral vertices. Diamond s topology classifies the network as a regular, Platonic structure-type. 

It appears that the 5 Platonic polyhedra obey Eqs. (1) and (2) of the text, if one specifies their topology by a Well s point symbol, given by A", in which n=A and p = a, and there is no relation between this polyhedral face symbol. A , and the computation of V, E and F in the Euler model of Eq. (1). It is also the case, that the 5 Platonic polyhedra... 

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