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There are five regular polyhedra: the tetrahedron, cube, octahedron, dodecahedron, and icosahedron. Versions of the tetrahedron, cube, and octahedron exist in every dimension, but the dodecahedron and icosahedron exist only in dimension three.
In dimension four, there are six regular polychora: the pentachoron, tesseract, 16-cell, 24-cell, 120-cell, and 600-cell. The pentachoron is an analog of the tetrahedron, and it has five tetrahedral cells. The tesseract is an analog of the cube, and it has eight cubical cells. The 16-cell is an analog of the octahedron, and it is bounded by 16 tetrahedra. The 24-cell is bounded by 24 octahedra, the 120-cell is bounded by 120 dodecahedra, and the 600-cell is bounded by 600 icosahedra.