3-space, the hexagonal tiling-triangular tiling honeycomb is a paracompact uniform honeycomb, constructed from triangular tiling, hexagonal tiling, and trihexagonal...

octahedron-hexagonal tiling honeycomb is a paracompact uniform honeycomb, constructed from octahedron, hexagonal tiling, and trihexagonal tiling cells, in...

The tetrahedral-octahedral honeycomb, alternated cubic honeycomb is a quasiregular space-filling tessellation (or honeycomb) in Euclidean 3-space. It...

tiling or tessellation in any number of dimensions. Its dimension can be clarified as n-honeycomb for a honeycomb of n-dimensional space. Honeycombs are...

uniform honeycomb in spherical space. The Schläfli symbol of the order-4 hexagonal tiling honeycomb is {6,3,4}. Since that of the hexagonal tiling is {6...

square tiling facets, with a mirrored sphenoid vertex figure. The runcinated order-4 octahedral honeycomb is the same as the runcinated square tiling honeycomb...

Hexagonal crystal system Hexagonal number Hexagonal tiling: a regular tiling of hexagons in a plane Hexagram: six-sided star within a regular hexagon...

the geometry of hyperbolic 3-space, the square tiling honeycomb is one of 11 paracompact regular honeycombs. It is called paracompact because it has infinite...

subgroup H2 tiling, the alternated order-4 hexagonal tiling, , with vertex figure (3.4)4. A lower symmetry form, index 6, of this honeycomb can be constructed...

and hexagonal close-packed (HCP), based on their symmetry. Both are based upon sheets of spheres arranged at the vertices of a triangular tiling; they...

of diamond, alum or fluorite are commonly octahedral, as the space-filling tetrahedral-octahedral honeycomb. The plates of kamacite alloy in octahedrite...

Euclidean 3-space) 1 p + 1 q = 1 2 : Euclidean plane tiling 1 p + 1 q < 1 2 : Hyperbolic plane tiling {\displaystyle {\begin{aligned}&{\frac {1}{p}}+{\frac...

rhombitrihexagonal tiling. A square symmetry projection forms two overlapping truncated square tiling, which combine together as a chamfered square tiling. The vertex...

up of hexagonal prisms. It is constructed from a hexagonal tiling extruded into prisms. It is one of 28 convex uniform honeycombs. This honeycomb can be...

on trihexagonal tiling planes, using the hexagon centers of the cuboctahedra, creating two triangular cupolae. This scaliform honeycomb is represented...

There are only 3 unique honeycombs from the square tiling, but all 6 tiling truncations are listed below for completeness, and tiling images are shown by...

cells. This honeycomb is also related to the 16-cell, cubic honeycomb, and order-4 hexagonal tiling honeycomb all which have octahedral vertex figures:...

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...

called bihedra, flat polyhedra, or doubly covered polygons. As a spherical tiling, a dihedron can exist as nondegenerate form, with two n-sided faces covering...

related to the cubic honeycomb, order-4 dodecahedral honeycomb, and order-4 hexagonal tiling honeycomb which all have octahedral vertex figures. It belongs...

represents the tetrahedral-octahedral honeycomb, with Coxeter graph filling space with alternately tetrahedral and octahedral cells. In 4 dimensions it...

geometry of hyperbolic 3-space, the order-4 square tiling honeycomb is one of 11 paracompact regular honeycombs. It is paracompact because it has infinite cells...

dodecahedral honeycomb which has all 12 faces as rhombi. It is a dual to the vertex-transitive gyrated tetrahedral-octahedral honeycomb. The rhombic pyramidal...

an example of the more general mathematical tiling or tessellation in any number of dimensions. Honeycombs are usually constructed in ordinary Euclidean...

Euclidean honeycombs (16-cell, 8-cell, 24-cell). Banchoff 2013, studied the decomposition of regular 4-polytopes into honeycombs of tori tiling the Clifford...

tetrahedral honeycomb Order-6 cubic honeycomb Order-6 dodecahedral honeycomb Hexagonal tiling honeycomb Order-4 hexagonal tiling honeycomb Order-5 hexagonal tiling...

uniform tilings Uniform tilings in hyperbolic plane Archimedean tiling Square tiling Triangular tiling Hexagonal tiling Truncated square tiling Snub square...

cell, and examples of a honeycomb are cubic honeycomb, order-5 cubic honeycomb, order-6 cubic honeycomb, and order-7 cubic honeycomb. The cube can be constructed...

octaplex (short for "octahedral complex"), icosatetrahedroid, octacube, hyper-diamond or polyoctahedron, being constructed of octahedral cells. The boundary...

rectified order-6 tetrahedral honeycomb, t1{3,3,6} has octahedral and triangular tiling cells arranged in a hexagonal prism vertex figure. Perspective...