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! |- valign=top align=center | 5-cell Pentatope 4-simplex | 16-cell Orthoplex 4-orthoplex | 8-cell Tesseract 4-cube |- ! ! ! |- valign=top align=center | Octaplex 24-cell | Dodecaplex 120-cell | Tetraplex 600-cell |} In geometry, a 4-polytope (sometimes also called a polychoron, polycell, or polyhedroid) is a four-dimensional polytope. It is a connected and closed figure, composed of lower-dimensional polytopal elements: vertices, edges, faces (polygons), and cells (polyhedra). Each face is shared by exactly two cells. The two-dimensional analogue of a 4-polytope is a polygon, and the three-dimensional analogue is a polyhedron. Topologically 4-polytopes are closely related to the uniform honeycombs, such as the cubic honeycomb, which tessellate 3-space; similarly the 3D cube is related to the infinite 2D square tiling. Convex 4-polytopes can be ''cut and unfolded'' as nets in 3-space. ==Definition== A 4-polytope is a closed four-dimensional figure. It comprises vertices (corner points), edges, faces and cells. A cell is the three-dimensional analogue of a face, and is therefore a polyhedron. Each face must join exactly two cells, analogous to the way in which each edge of a polyhedron joins just two faces. Like any polytope, the elements of a 4-polytope cannot be subdivided into two or more sets which are also 4-polytopes, i.e. it is not a compound. The most familiar 4-polytope is the tesseract or hypercube, the 4D analogue of the cube. 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「4-polytope」の詳細全文を読む スポンサード リンク
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