Face-regular bifaced polyhedra (Q5935437)
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scientific article; zbMATH DE number 1610264
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Face-regular bifaced polyhedra |
scientific article; zbMATH DE number 1610264 |
Statements
Face-regular bifaced polyhedra (English)
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22 July 2002
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regularity
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fullerenes
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polyhedra
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edge-adjacency
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face-regular bifaced polyhedra
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The authors consider polyhedra with two types of faces: \(p_a\) \(a\)-gons and \(p_b\) \(b\)-gons. Moreover, these polyhedra satisfy one of the following conditions:NEWLINENEWLINENEWLINE\(\bullet\) \(aR_i\): each \(a\)-gonal face is adjacent to \(i\) \(a\)-gonal faces;NEWLINENEWLINENEWLINE\(\bullet\) \(bR_j\): each \(b\)-gonal face is adjacent to \(j\) \(b\)-gonal faces.NEWLINENEWLINENEWLINEIf the graph \(G_a\) (resp. \(G_b)\) of the edge-adjacency of \(a\)-faces (resp. \(b\)-faces) is regular, then the polyhedra are called face-regular bifaced polyhedra. Fullerenes are well-known similar polyhedra.NEWLINENEWLINENEWLINEUnder the assumption \(3\leq a<b\), \(0<p_a\), \(0\leq p_b\) the authors classify these polyhedra except for certain cases of type \(aR_0\) and \(aR_1\).
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