Automorphism geometric

POFs Xo nd Xi correspond to the two enantiomers shown in Figure 4.3. POF X2 is not chemically realizable. However, it is geometrically realizable Any planar placement of the five atoms has the POF X2-b There are 3 = 729 abstract POFs for structure 4.2b, cyclohexane. Each of the 6 selected increasing quadruples can have the orientation plus, minus, or zero independently. However, cyclohexane has 12 graph automorphisms. Considering relabelings according to these permutations, some of the abstract POFs are isomor-... 

Regular geometrical shape Automorphous Idiomorphous Euhedral ... 

It follows that an automorphism of an abstract simplicial complex induces a continuous automorphism of its geometric realization, and that the geometric realizations of two isomorphic abstract simplicial complexes are homeo-morphic, with homeomorphisms induced by the isomorphism maps. On the other hand, the existence of a homeomorphism between Z i and A2 does not imply the isomorphism of A and. 2. If a topological space allows a simplicial structure, then it allows infinitely many nonisomorphic simplicial structures. 

Algorithm 13 Construction of the Geometrically Distinct Topological Automorphisms (Adapted from Ref. 7)... 

Use of geometrical attributes table (GAT) and geometrically distinct topological automorphism (GDTA). 

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