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Mucube: {4,6|4}: 6 squares about each vertex (related to cubic honeycomb, constructed by cubic cells, removing two opposite faces from each, and linking sets of six together around a faceless cube.) Muoctahedron : {6,4|4}: 4 hexagons about each vertex (related to bitruncated cubic honeycomb , constructed by truncated octahedron with their ...
In geometry, a skew apeirohedron is an infinite skew polyhedron consisting of nonplanar faces or nonplanar vertex figures, allowing the figure to extend indefinitely without folding round to form a closed surface. Skew apeirohedra have also been called polyhedral sponges.
An n-apeirotope is an infinite n-polytope: a 2-apeirotope or apeirogon is an infinite polygon, a 3-apeirotope or apeirohedron is an infinite polyhedron, etc. There are two main geometric classes of apeirotope: [15] Regular honeycombs in n dimensions, which completely fill an n-dimensional space.
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Regular polyhedron. Platonic solid: . Tetrahedron, Cube, Octahedron, Dodecahedron, Icosahedron; Regular spherical polyhedron. Dihedron, Hosohedron; Kepler–Poinsot ...
The elements of a polytope can be considered according to either their own dimensionality or how many dimensions "down" they are from the body.
An abstract n-polytope is a partially ordered set P (whose elements are called faces) such that P contains a least face and a greatest face, each maximal totally ordered subset (called a flag) contains exactly n + 2 faces, P is strongly connected, and there are exactly two faces that lie strictly between a and b are two faces whose ranks differ by two.
A regular polyhedron is a polyhedron whose symmetry group acts transitively on its flags.A regular polyhedron is highly symmetrical, being all of edge-transitive, vertex-transitive and face-transitive.