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In geometry and combinatorics, a simplicial (or combinatorial) ''d''-sphere is a simplicial complex homeomorphic to the ''d''-dimensional sphere. Some simplicial spheres arise as the boundaries of convex polytopes, however, in higher dimensions most simplicial spheres cannot be obtained in this way. The most important open problem in the field is the g-conjecture, formulated by Peter McMullen, which asks about possible numbers of faces of different dimensions of a simplicial sphere. == Examples == * For any ''n'' ≥ 3, the simple ''n''-cycle ''C''''n'' is a simplicial circle, i.e. a simplicial sphere of dimension 1. This construction produces all simplicial circles. * The boundary of a convex polyhedron in R3 with triangular faces, such as an octahedron or icosahedron, is a simplicial 2-sphere. * More generally, the boundary of any (''d''+1)-dimensional compact (or bounded) simplicial convex polytope in the Euclidean space is a simplicial sphere. 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「Simplicial sphere」の詳細全文を読む スポンサード リンク
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