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In four-dimensional geometry, a 16-cell, is a regular convex 4-polytope. It is one of the six regular convex 4-polytopes first described by the Swiss mathematician Ludwig Schläfli in the mid-19th century. It is also called C16, hexadecachoron, or hexdecahedroid.〔Matila Ghyka, ''The Geometry of Art and Life'' (1977), p.68〕 It is a part of an infinite family of polytopes, called cross-polytopes or ''orthoplexes''. The dual polytope is the tesseract (4-cube). Conway's name for a cross-polytope is orthoplex, for ''orthant complex''. The 16-cell has 16 cells as the tesseract has 16 vertices. ==Geometry== It is bounded by 16 cells, all of which are regular tetrahedra. It has 32 triangular faces, 24 edges, and 8 vertices. The 24 edges bound 6 squares lying in the 6 coordinate planes. The eight vertices of the 16-cell are (±1, 0, 0, 0), (0, ±1, 0, 0), (0, 0, ±1, 0), (0, 0, 0, ±1). All vertices are connected by edges except opposite pairs. The Schläfli symbol of the 16-cell is . Its vertex figure is a regular octahedron. There are 8 tetrahedra, 12 triangles, and 6 edges meeting at every vertex. Its edge figure is a square. There are 4 tetrahedra and 4 triangles meeting at every edge. The 16-cell can be decomposed into two similar disjoint circular chains of eight tetrahedrons each, four edges long. Each chain, when stretched out straight, forms a Boerdijk–Coxeter helix. This decomposition can be seen in a 4-4 duoantiprism construction of the ''16-cell'': or , Schläfli symbol ⨂ or ss, symmetry [ The ''16-cell'' can be dissected into two octahedral pyramids, which share a new octahedron base through the 16-cell center. 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「16-cell」の詳細全文を読む スポンサード リンク
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