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Oblate Cubille
In geometry, the trigonal trapezohedral honeycomb is a Uniform honeycomb, uniform space-filling tessellation (or honeycomb (geometry), honeycomb) in Euclidean 3-space. Cells are identical trigonal trapezohedra or rhombohedra. Conway, Burgiel, and Goodman-Strauss call it an oblate cubille. Related honeycombs and tilings This honeycomb can be seen as a rhombic dodecahedral honeycomb, with the rhombic dodecahedron, rhombic dodecahedra dissection (geometry), dissected with its center into 4 trigonal trapezohedron, trigonal trapezohedra or rhombohedron, rhombohedra. It is analogous to the regular hexagonal being dissectable into 3 rhombi and tiling the plane as a rhombille. The rhombille tiling is actually an orthogonal projection of the ''trigonal trapezohedral honeycomb''. A different orthogonal projection produces the quadrille (geometry), quadrille where the rhombi are distorted into squares. Dual tiling It is dual to the quarter cubic honeycomb with tetrahedral and truncat ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Uniform Honeycomb
In geometry, a uniform honeycomb or uniform tessellation or infinite uniform polytope, is a vertex-transitive honeycomb made from uniform polytope facets. All of its vertices are identical and there is the same combination and arrangement of faces at each vertex. Its dimension can be clarified as -honeycomb for an -dimensional honeycomb. An -dimensional uniform honeycomb can be constructed on the surface of -spheres, in -dimensional Euclidean space, and -dimensional hyperbolic space. A 2-dimensional uniform honeycomb is more often called a uniform tiling or uniform tessellation. Nearly all uniform tessellations can be generated by a Wythoff construction, and represented by a Coxeter–Dynkin diagram. The terminology for the convex uniform polytopes used in uniform polyhedron, uniform 4-polytope, uniform 5-polytope, uniform 6-polytope, uniform tiling, and convex uniform honeycomb articles were coined by Norman Johnson. Wythoffian tessellations can be defined by a vertex figure. ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
