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In geometry, the rhombicuboctahedron, or small rhombicuboctahedron, is an Archimedean solid with eight triangular and eighteen square faces. There are 24 identical vertices, with one triangle and three squares meeting at each. (Note that six of the squares only share vertices with the triangles while the other twelve share an edge.) The polyhedron has octahedral symmetry, like the cube and octahedron. Its dual is called the deltoidal icositetrahedron or trapezoidal icositetrahedron, although its faces are not really true trapezoids. The name ''rhombicuboctahedron'' refers to the fact that twelve of the square faces lie in the same planes as the twelve faces of the rhombic dodecahedron which is dual to the cuboctahedron. ''Great rhombicuboctahedron'' is an alternative name for a truncated cuboctahedron, whose faces are parallel to those of the (small) rhombicuboctahedron. It can also be called an ''expanded cube'' or ''cantellated cube'' or a ''cantellated octahedron'' from truncation operations of the uniform polyhedron. ==Geometric relations== There are distortions of the rhombicuboctahedron that, while some of the faces are not regular polygons, are still vertex-uniform. Some of these can be made by taking a cube or octahedron and cutting off the edges, then trimming the corners, so the resulting polyhedron has six square and twelve rectangular faces. These have octahedral symmetry and form a continuous series between the cube and the octahedron, analogous to the distortions of the rhombicosidodecahedron or the tetrahedral distortions of the cuboctahedron. However, the rhombicuboctahedron also has a second set of distortions with six rectangular and sixteen trapezoidal faces, which do not have octahedral symmetry but rather Th symmetry, so they are invariant under the same rotations as the tetrahedron but different reflections. The lines along which a Rubik's Cube can be turned are, projected onto a sphere, similar, topologically identical, to a rhombicuboctahedron's edges. In fact, variants using the Rubik's Cube mechanism have been produced which closely resemble the rhombicuboctahedron. The rhombicuboctahedron is used in three uniform space-filling tessellations: the cantellated cubic honeycomb, the runcitruncated cubic honeycomb, and the runcinated alternated cubic honeycomb. 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「rhombicuboctahedron」の詳細全文を読む スポンサード リンク
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