In three-dimensional hyperbolic geometry, the alternated hexagonal tiling honeycomb, h{6,3,3}, or , is a semiregular tessellation with tetrahedron and triangular tiling cells arranged in an octahedron vertex figure. It is named after its construction, as an alteration of a hexagonal tiling honeycomb.
A geometric honeycomb is a space-filling of polyhedral or higher-dimensional cells, so that there are no gaps. It is an example of the more general mathematical tiling or tessellation in any number of dimensions.
Honeycombs are usually constructed in ordinary Euclidean ("flat") space, like the convex uniform honeycombs. They may also be constructed in non-Euclidean spaces, such as hyperbolic uniform honeycombs. Any finite uniform polytope can be projected to its circumsphere to form a uniform honeycomb in spherical space.
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symbol of the hexagonaltilinghoneycomb is {6,3,3}. Since that of the hexagonaltiling is {6,3}, this honeycomb has three such hexagonaltilings meeting at...
geometry, the alternatedhexagonaltilinghoneycomb, h{6,3,3}, or , is a semiregular tessellation with tetrahedron and triangular tiling cells arranged...
is one of three regular tilings of the plane. The other two are the triangular tiling and the square tiling. Hexagonaltiling is the densest way to arrange...
on trihexagonal tiling planes, using the hexagon centers of the cuboctahedra, creating two triangular cupolae. This scaliform honeycomb is represented...
Conway calls it a hexadeltille, combining alternate elements from a hexagonaltiling (hextille) and triangular tiling (deltille). Kagome (Japanese: 籠目) is...
Hexagonal crystal system Hexagonal number Hexagonaltiling: a regular tiling of hexagons in a plane Hexagram: six-sided star within a regular hexagon...
wallpaper groups. A tiling that lacks a repeating pattern is called "non-periodic". An aperiodic tiling uses a small set of tile shapes that cannot form...
cells. Twenty-eight such honeycombs are known: the familiar cubic honeycomb and 7 truncations thereof; the alternated cubic honeycomb and 4 truncations thereof;...
The alternated square tilinghoneycomb, h{4,4,3}, is a quasiregular paracompact uniform honeycomb in hyperbolic 3-space. It has cube and square tiling facets...
regular tilings of the plane. The other two are the square tiling and the hexagonaltiling. There are 9 distinct uniform colorings of a triangular tiling. (Naming...
up of hexagonal prisms. It is constructed from a hexagonaltiling extruded into prisms. It is one of 28 convex uniform honeycombs. This honeycomb can be...
must have at least three sides. When considering polyhedra as a spherical tiling, this restriction may be relaxed, since digons (2-gons) can be represented...
icosidodecahedron and hexagonal prism cells, with a phyllic disphenoid vertex figure. Centered on hexagonal prism The omnisnub icosahedral honeycomb, h(t0,1,2,3{3...
In geometry, the hexagonal prism is a prism with hexagonal base. Prisms are polyhedrons; this polyhedron has 8 faces, 18 edges, and 12 vertices. Since...
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