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" TITLE="5">)〔Regular polytopes, pp.49-50, p.98〕 |- |bgcolor=#e7dcc3|Stellation core||rhombic triacontahedron |- |bgcolor=#e7dcc3|Convex hull||Dodecahedron |- |bgcolor=#e7dcc3|Index||UC9 |- |bgcolor=#e7dcc3|Polyhedra||5 cubes |- |bgcolor=#e7dcc3|Faces||30 squares |- |bgcolor=#e7dcc3|Edges||60 |- |bgcolor=#e7dcc3|Vertices||20 |- |bgcolor=#e7dcc3|Dual||Compound of five octahedra |- |bgcolor=#e7dcc3|Symmetry group||icosahedral (''I''h) |- |bgcolor=#e7dcc3|Subgroup restricting to one constituent||pyritohedral (''T''h) |} The compound of five cubes is one of the five regular polyhedral compounds. This compound was first described by Edmund Hess in 1876. It is one of five regular compounds, and dual to the compound of five octahedra. It can be seen as a faceting of a regular dodecahedron. It is one of the stellations of the rhombic triacontahedron. It has icosahedral symmetry (Ih). ==Geometry== The compound is a faceting of a dodecahedron. Each cube represents one orientation of 8 of 12 vertices within a dodecahedron convex hull. If the shape is considered as a union of five cubes yielding a simple concave solid without self-intersecting surfaces, then it has 360 faces (all triangles), 182 vertices (60 with degree 3, 30 with degree 4, 12 with degree 5, 60 with degree 8, and 20 with degree 12), and 540 edges, yielding an Euler characteristic of 182-540+360 = +2. 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「compound of five cubes」の詳細全文を読む スポンサード リンク
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