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- W1966134672 abstract "Call bifaced any k-valent polyhedron, whose faces are pa a-gons and pb b-gons only, where 3⩽a<b, 0<pa, 0⩽pb. We consider the case b⩽2k/(k−2) covering applications; so either k=3⩽a<b⩽6, or (k;a,b,pa)=(4;3,4,8). Call such a polyhedron aRi (resp., bRj) if each of its a-gonal (b-gonal) faces is adjacent to exactly i a-gonal (resp., j b-gonal) faces. The preferable (i.e., with isolated pentagons) fullerenes are the case aR0 for (k;a,b)=(3;5,6). We classify all a- or b-face-regular bifaced polyhedra, except aR0 for (k;a,b)=(3;4,6),(3;5,6),(4;3,4) and aR1 for (k;a,b)=(3;5,6),(4;3,4). For example, we list all 13,6,4,10,26 polyhedra bRj for all five possible cases: k=4; k=3,b<6; k=3,b=6,a=3,4,5." @default.
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- W1966134672 date "2001-05-01" @default.
- W1966134672 modified "2023-10-18" @default.
- W1966134672 title "Face-regular bifaced polyhedra" @default.
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- W1966134672 doi "https://doi.org/10.1016/s0378-3758(00)00287-1" @default.
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