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In four-dimensional geometry, a runcinated 5-cell is a convex uniform 4-polytope, being a runcination (a 3rd order truncation) of the regular 5-cell. There are 3 unique degrees of runcinations of the 5-cell, including with permutations, truncations, and cantellations. ==Runcinated 5-cell== 30 |- |bgcolor=#e7dcc3|Edges |colspan=2|60 |- |bgcolor=#e7dcc3|Vertices |colspan=2|20 |- |bgcolor=#e7dcc3|Vertex figure |colspan=2|80px (Elongated equilateral-triangular antiprism) |- |bgcolor=#e7dcc3|Symmetry group |colspan=2|Aut(A4), , order 240 |- |bgcolor=#e7dcc3|Properties |colspan=2|convex, isogonal isotoxal |- |bgcolor=#e7dcc3|Uniform index |colspan=2|''4'' 5 ''6'' |} The runcinated 5-cell or small prismatodecachoron is constructed by expanding the cells of a 5-cell radially and filling in the gaps with triangular prisms (which are the face prisms and edge figures) and tetrahedra (cells of the dual 5-cell). It consists of 10 tetrahedra and 20 triangular prisms. The 10 tetrahedra correspond with the cells of a 5-cell and its dual. E. L. Elte identified it in 1912 as a semiregular polytope. 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「Runcinated 5-cell」の詳細全文を読む スポンサード リンク
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