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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.
A uniform polyhedron is a polyhedron in which the faces are regular and they are isogonal; examples include Platonic and Archimedean solids as well as prisms and antiprisms. [4] The Johnson solids are named after American mathematician Norman Johnson (1930–2017), who published a list of 92 such polyhedra in 1966.
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.
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 ...
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 ).
3.3.3.3.4: 32 triangles 6 squares 60 24 O Icosidodecahedron: 3.5.3.5: 20 triangles 12 pentagons: 60 30 I h: Truncated dodecahedron: 3.10.10: 20 triangles 12 decagons: 90 60 I h: Truncated icosahedron: 5.6.6: 12 pentagons 20 hexagons 90 60 I h: Rhombicosidodecahedron: 3.4.5.4: 20 triangles 30 squares 12 pentagons 120 60 I h: Truncated ...
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: ...