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  • Coxeter–Dynkin diagram — See also: Dynkin diagram Coxeter Dynkin diagrams for the fundamental finite Coxeter groups …   Wikipedia

  • Point group — The Bauhinia blakeana flower on the Hong Kong flag has C5 symmetry; the star on each petal has D5 symmetry. In geometry, a point group is a group of geometric symmetries (isometries) that keep at least one point fixed. Point groups can exist in a …   Wikipedia

  • Convex uniform honeycombs in hyperbolic space — The {5,3,4} honeycomb in 3D hyperbolic space, viewed in perspective In geometry, a convex uniform honeycomb is a tessellation of convex uniform polyhedron cells. In 3 dimensional hyperbolic space there are nine Coxeter group f …   Wikipedia

  • Convex uniform honeycomb — The alternated cubic honeycomb is one of 28 space filling uniform tessellations in Euclidean 3 space, composed of alternating yellow tetrahedra and red octahedra. In geometry, a convex uniform honeycomb is a uniform tessellation which fills three …   Wikipedia

  • Alternated hypercubic honeycomb — An alternated square tiling is another square tiling, but having two types of squares, alternating in a checkerboard pattern …   Wikipedia

  • Omnitruncated 5-simplex honeycomb — (No image) Type Uniform honeycomb Family Omnitruncated simplectic honeycomb Schläfli symbol t0,1,2,3,4,5{3[6]} Coxeter–Dynkin diagrams …   Wikipedia

  • Demihypercube — Not to be confused with Hemicube (geometry). Alternation of the n cube yields one of two n demicubes, as in this 3 dimensional illustration of the two tetrahedra that arise as the 3 demicubes of the 3 cube. In geometry, demihypercubes (also… …   Wikipedia

  • Omnitruncation — In geometry, an omnitruncation is an operation applied to a regular polytope (or honeycomb) in a Wythoff construction that creates a maximum number of facets. It is represented in a Coxeter–Dynkin diagram with all nodes ringed. It is a shortcut… …   Wikipedia

  • 16-cell honeycomb — Perspective projection: the first layer of adjacent 16 cell facets. Type Regular 4 space honeycomb Family Alternated hypercube honeycomb Schläfli symbol {3,3,4,3} h{4,3,3,4} …   Wikipedia

  • Coxeter group — In mathematics, a Coxeter group, named after H.S.M. Coxeter, is an abstract group that admits a formal description in terms of mirror symmetries. Indeed, the finite Coxeter groups are precisely the finite Euclidean reflection groups; the symmetry …   Wikipedia

  • 16-cell — Regular hexadecachoron (16 cell) (4 orthoplex) Schlegel diagram (vertices and edges) Type Convex regular 4 polytope Schläfli symbo …   Wikipedia

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