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A Zoo of l_1embeddable Polytopal Graphs
, 1996
"... A simple graph G = (V; E) is called l 1 graph if, for some ,n 2 IN , there exists a vertexaddressing of each vertex v of G by a vertex a(v) of the n cube H n preserving, up to the scale , the graph distance, i.e. dG (v; v 0 ) = dHn (a(v); a(v 0 )) for all v 2 V . We distinguish l 1 graphs ..."
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A simple graph G = (V; E) is called l 1 graph if, for some ,n 2 IN , there exists a vertexaddressing of each vertex v of G by a vertex a(v) of the n cube H n preserving, up to the scale , the graph distance, i.e. dG (v; v 0 ) = dHn (a(v); a(v 0 )) for all v 2 V . We distinguish l 1 graphs between 1skeletons of a variety of well known classes of polytopes: semiregular, regularfaced, zonotopes, Delaunay polytopes of dimension 4 and several generalizations of prisms and antiprisms.
Fullerenes and Coordination Polyhedra versus HalfCubes Embeddings
, 1997
"... A fullerene F n is a 3regular (or cubic) polyhedral carbon molecule for which the n vertices  the carbons atoms  are arranged in 12 pentagons and ( n 2 \Gamma 10) hexagons. Only a finite number of fullerenes are expected to be, up to scale, isometrically embeddable into a hypercube. Looking fo ..."
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A fullerene F n is a 3regular (or cubic) polyhedral carbon molecule for which the n vertices  the carbons atoms  are arranged in 12 pentagons and ( n 2 \Gamma 10) hexagons. Only a finite number of fullerenes are expected to be, up to scale, isometrically embeddable into a hypercube. Looking for the list of such fullerenes, we first check the embeddability of all fullerenes F n for n ! 60 and of all preferable fullerenes C n for n ! 86 and their duals. Then, we consider some infinite families, including fullerenes with icosahedral symmetry, which describe virus capsids, onionlike metallic clusters and geodesic domes. Quasiembeddings and fullerene analogues are considered. We also present some results on chemically relevant polyhedra such as coordination polyhedra and cluster polyhedra. Finally we conjecture that the list of known embeddable fullerenes is complete and present its relevance to the Katsura model for vesicles cells.
THE SPECIAL CUTS OF 600CELL
, 708
"... Abstract. A polytope is called regular faced if every one of its facets is a regular polytope. The 4dimensional regularfaced polytopes were determined by [2, 3, 1]. The last class of such poytopes are the one obtained by removing a set of nonadjacent vertices of 600cell. Here we determine all su ..."
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Abstract. A polytope is called regular faced if every one of its facets is a regular polytope. The 4dimensional regularfaced polytopes were determined by [2, 3, 1]. The last class of such poytopes are the one obtained by removing a set of nonadjacent vertices of 600cell. Here we determine all such independent sets up to isomorphism and find 314248344 polytopes. 1.