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Non-crystallographic symmetry of two extreme variants of decomposition of 4-dimensional polyhedron into linear substructures

1Rabinovich A.L.,
2Talis A.L.

1IKarelian Research Centre of Russian Academy of Sciences
2Institute of organoelement compounds RAS
A group-theoretical description of two mappings from 4-dimensional 240-vertex polyhedron into 3-dimensional Euclidean space which were obtained by the Hopf fibration (a system of channel-like structures and a complex of tetrahedrally coordinated chains and tetrahelices) has been suggested. It was shown that both systems can be ideal prototypes for real structures.
English version is available upon request
Architecture and symmetry of a combination of dissimilar tetrahedrally coordinated chains 1Rabinovich A.L.,
2Talis A.L.
1IKarelian Research Centre of Russian Academy of Sciences
2Institute of organoelement compounds RAS
Dissimilar tetrahedrally coordinated chain substructures have been considered as mappings from 4-dimensional 240-vertex polyhedron (the polytope {240}) into 3-dimensional Euclidean space by the Hopf fibration. A group-theoretical description of a combination of these substructures has been obtained.
English version is available upon request
Characterization of non-crystallographic symmetry of linear substructures that are mappings from a 4-dimensional diamond-like polytope 1Talis A.L., 2Rabinovich A.L. 1Institute of organoelement compounds RAS
2Karelian Research Centre of Russian Academy of Sciences
A polyhedron in 4-dimensional Euclidean space (polytope {240}) containing 240 tetrahedrally coordinated vertices is considered. The Hopf fibration for the polytope {240} allows constructing a number of its linear substructures. An approach for the group-theoretical description of aggregates of these substructures has been suggested. The desired symmetry groups are isomorphic to subgroups of the permutation group of vertices of the {240} polytope English version is available upon request
Architecture and symmetry of a union of tetrahedrally coordinated chain substructures in a cylindrical corrugated surface 1Talis A.L., 2Rabinovich A.L. 1Institute of organoelement compounds RAS
2Karelian Research Centre of Russian Academy of Sciences
Polytope {240} - a polyhedron in 4-dimensional Euclidean space containing 240 tetrahedrally coordinated vertices is considered. Tetrahedrally coordinated chain substructures as mappings from the polyhedron into 3-dimensional Euclidean space forming a cylindrical corrugated surface have been distinguished. A group-theoretical description of an aggregate of these substructures has been suggested English version is available upon request
         
         
       

 



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