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| Grand 600-cell ： ウィキペディア英語版 |
Grand 600-cell
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|bgcolor=#e7dcc3|Edges||720
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|bgcolor=#e7dcc3|Vertices||120
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|bgcolor=#e7dcc3|Vertex figure||
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|bgcolor=#e7dcc3|Schläfli symbol||
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|bgcolor=#e7dcc3|Coxeter-Dynkin diagram||
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|bgcolor=#e7dcc3|Symmetry group||H4, ()
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|bgcolor=#e7dcc3|Dual|| Great grand stellated 120-cell
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|bgcolor=#e7dcc3|Properties|| Regular
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In geometry, the grand 600-cell or grand polytetrahedron is a regular star 4-polytope with Schläfli symbol . It is one of 10 regular Schläfli-Hess polytopes. It is the only one with 600 cells.
It is one of four ''regular star 4-polytopes'' discovered by Ludwig Schläfli. It is named by John Horton Conway, extending the naming system by Arthur Cayley for the Kepler-Poinsot solids.
== Related polytopes ==
It has the same edge arrangement as the great stellated 120-cell, and grand stellated 120-cell, and same face arrangement as the great icosahedral 120-cell. As the only stellation of the 600-cell among the Schläfli-Hess polytopes, it could be taken as analogous to the three-dimensional great icosahedron, the only stellation of the icosahedron among the Kepler-Poinsot polyhedra. Indeed, the great 600-cell is dual to the great grand stellated 120-cell, which could be taken as a 4D analogue of the great stellated dodecahedron, dual of the great icosahedron.
抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』
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