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In geometry, the hexagonal tiling or hexagonal tessellation is a regular tiling of the Euclidean plane, in which exactly three hexagons meet at each vertex. It has Schläfli symbol of {6,3} or t {3,6} (as a truncated triangular tiling).
Regular, quasiregular. In the field of hyperbolic geometry, the order-6 hexagonal tiling honeycomb is one of 11 regular paracompact honeycombs in 3-dimensional hyperbolic space. It is paracompact because it has cells with an infinite number of faces. Each cell is a hexagonal tiling whose vertices lie on a horosphere: a flat plane in hyperbolic ...
Thus a triangular tiling of fundamental units will be generated that is mutually locally derivable from the tiling by the colored tiles. The other figure drawn onto the tiling, the white hexagon, represents a primitive cell of the tiling. Copies of the corresponding patch of coloured tiles can be translated to form an infinite tiling of the ...
Each infinite cell consists of an order-6 hexagonal tiling whose vertices lie on a 2-hypercycle, each of which has a limiting circle on the ideal sphere. The Schläfli symbol of the order-8-3 hexagonal honeycomb is {6,8,3}, with three order-5 hexagonal tilings meeting at each edge. The vertex figure of this honeycomb is an octagonal tiling, {8,3}.
Euclidean tilings by convex regular polygons. A regular tiling has one type of regular face. A semiregular or uniform tiling has one type of vertex, but two or more types of faces. A k -uniform tiling has k types of vertices, and two or more types of regular faces. A non-edge-to-edge tiling can have different-sized regular faces.
Uniform colorings. There are a total of 32 uniform colorings of the 11 uniform tilings: Triangular tiling – 9 uniform colorings, 4 wythoffian, 5 nonwythoffian. Square tiling – 9 colorings: 7 wythoffian, 2 nonwythoffian. Hexagonal tiling – 3 colorings, all wythoffian. Trihexagonal tiling – 2 colorings, both wythoffian.
In the geometry of hyperbolic 3-space, the order-6-6 hexagonal honeycomb (or 6,6,6 honeycomb) is a regular space-filling tessellation (or honeycomb) with Schläfli symbol {6,6,6}. It has six order-6 hexagonal tilings, {6,6}, around each edge. All vertices are ultra-ideal (existing beyond the ideal boundary) with infinitely many hexagonal ...
Order-6 tetrakis square tiling. Properties. Vertex-transitive. In geometry, the truncated order-4 hexagonal tiling is a uniform tiling of the hyperbolic plane. It has Schläfli symbol of t {6,4}. A secondary construction tr {6,6} is called a truncated hexahexagonal tiling with two colors of dodecagons .