The construction of cubic and quartic planar maps with prescribed face degrees

AbstractIn this paper, the existence and availability of computer programs to constructively enumerate all simple connected cubic or quartic planar maps with prescribed number of vertices and face degrees is announced and results of the programs are presented. The underlying algorithms of the computer programs are described

トポロジー的織込み構造の構成と分類

Tohoku University小谷元子課

Lists of Face-Regular Polyhedra

We introduce a new notion that connects the combinatorial concept of regularity with the geometrical notion of face transitivity. This new notion implies finiteness results in the case of bounded maximal face size. We give lists of structures for some classes and investigate polyhedra with constant vertex degrees and faces of only two sizes