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[W] Wenninger, 1974, has 119 figures: 1–5 for the Platonic solids, 6–18 for the Archimedean solids, 19–66 for stellated forms including the 4 regular nonconvex polyhedra, and ended with 67–119 for the nonconvex uniform polyhedra.
Augmentation involves attaching the Johnson solids onto one or more faces of polyhedra, while elongation or gyroelongation involve joining them onto the bases of a prism or antiprism, respectively. Some others are constructed by diminishment, the removal of one of the first six solids from one or more of a polyhedron's faces. [6]
3.4 Catalan solids. ... 6.1 Honeycombs. ... A polytope is a geometric object with flat sides, which exists in any general number of dimensions.
15 are in the regular H 4 [3,3,5] group (120-cell/600-cell) family. 1 special snub form in the [3,4,3] group family. 1 special non-Wythoffian 4-polytope, the grand antiprism. TOTAL: 68 − 4 = 64; These 64 uniform 4-polytopes are indexed below by George Olshevsky. Repeated symmetry forms are indexed in brackets.
Edge, a 1-dimensional element; Face, a 2-dimensional element; Cell, a 3-dimensional element; Hypercell or Teron, a 4-dimensional element; Facet, an (n-1)-dimensional element; Ridge, an (n-2)-dimensional element; Peak, an (n-3)-dimensional element; For example, in a polyhedron (3-dimensional polytope), a face is a facet, an edge is a ridge, and ...
In geometry, a 4-polytope (sometimes also called a polychoron, [1] polycell, or polyhedroid) is a four-dimensional polytope. [ 2 ] [ 3 ] It is a connected and closed figure, composed of lower-dimensional polytopal elements: vertices , edges , faces ( polygons ), and cells ( polyhedra ).
4 6: 10: 18: 1: 7: 4: ... There are 4 regular projective polyhedra related to 4 of 5 Platonic solids. ... There are two main geometric classes of apeirotope: ...
Each convex regular 4-polytope is bounded by a set of 3-dimensional cells which are all Platonic solids of the same type and size. These are fitted together along their respective faces (face-to-face) in a regular fashion, forming the surface of the 4-polytope which is a closed, curved 3-dimensional space (analogous to the way the surface of ...