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Let be a metric space with distance function .Let be a set of indices and let () be a tuple (indexed collection) of nonempty subsets (the sites) in the space .The Voronoi cell, or Voronoi region, , associated with the site is the set of all points in whose distance to is not greater than their distance to the other sites , where is any index different from .
A 3-dimensional uniform honeycomb is a honeycomb in 3-space composed of uniform polyhedral cells, and having all vertices the same (i.e., the group of [isometries of 3-space that preserve the tiling] is transitive on vertices). There are 28 convex examples in Euclidean 3-space, [1] also called the Archimedean honeycombs.
Tessellation using Texas-shaped non-convex 12-sided polygons. If only one shape of tile is allowed, tilings exist with convex N-gons for N equal to 3, 4, 5, and 6. For N = 5, see Pentagonal tiling, for N = 6, see Hexagonal tiling, for N = 7, see Heptagonal tiling and for N = 8, see octagonal tiling.
Download as PDF; Printable version; In other projects ... This is a list of tessellations. ... 3 5.4 s{3,8} Order-7 triangular tiling ...
It is composed of rhombicuboctahedra, truncated cubes, octagonal prisms, and cubes in a ratio of 1:1:3:3, with an isosceles-trapezoidal pyramid vertex figure. Its name is derived from its Coxeter diagram , with three ringed nodes representing 3 active mirrors in the Wythoff construction from its relation to the regular cubic honeycomb.
Download as PDF; Printable version; In other projects Wikidata item; Appearance. move to sidebar hide. A uniform tessellation may be: A uniform tiling in two ...
Download as PDF; Printable version; ... (3 P, 1 F) H. Honeycombs (geometry) ... Pages in category "Tessellation" The following 43 pages are in this category, out of ...
A 3 W 2 G 28 t 1,2 δ 4 bc [[4,3,4]] Truncated octahedrille (Bitruncated cubic honeycomb) Tetragonal disphenoid: Oblate tetrahedrille: Tetragonal disphenoid: J 17 A 18 W 13 G 25 t 0,1,2 δ 4 nc [4,3,4] n-tCO-trille (Cantitruncated cubic honeycomb) Mirrored sphenoid: Triangular pyramidille: Mirrored sphenoid, , J 18 A 19 W 19 G 20 t 0,1,3 δ 4 ...