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In geometry, runcination is an operation that cuts a regular polytope (or honeycomb) simultaneously along the faces, edges and vertices, creating new facets in place of the original face, edge, and vertex centers. It is a higher order truncation operation, following cantellation, and truncation. It is represented by an extended Schläfli symbol t0,3. This operation only exists for 4-polytopes or higher. This operation is dual-symmetric for regular uniform 4-polytopes and 3-space convex uniform honeycombs. For a regular 4-polytope, the original cells remain, but become separated. The gaps at the separated faces become p-gonal prisms. The gaps between the separated edges become r-gonal prisms. The gaps between the separated vertices become cells. The vertex figure for a regular 4-polytope is an ''q''-gonal antiprism (called an ''antipodium'' if ''p'' and ''r'' are different). For regular 4-polytopes/honeycombs, this operation is also called expansion by Alicia Boole Stott, as imagined by taking the cells of the regular form moving them away from the center and filling in new faces in the gaps for each opened vertex and edge. Runcinated 4-polytopes/honeycombs forms: ||Runcinated 16-cell (Same as runcinated 8-cell)||80px ||80px80px |- |align=center|t0,3 ||Runcinated 24-cell||80px ||80px |- |align=center|t0,3 ||Runcinated 120-cell (Same as runcinated 600-cell)||80px |80px |- !colspan=4|Euclidean convex uniform honeycombs |- |align=center|t0,3 ||Runcinated cubic honeycomb (Same as cubic honeycomb)||80px |80px |- !colspan=4|Hyperbolic uniform honeycombs |- |align=center|t0,3 ||Runcinated order-5 cubic honeycomb||80px|| |- |align=center|t0,3 ||Runcinated icosahedral honeycomb||80px|| |- |align=center|t0,3 ||Runcinated order-5 dodecahedral honeycomb||80px|| |} == See also == * uniform polyhedron * uniform 4-polytope * Rectification (geometry) * Truncation (geometry) * Cantellation (geometry) 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「Runcination」の詳細全文を読む スポンサード リンク
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