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...

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...

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

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...

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

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

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...

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...

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...

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

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

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...

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...

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

order-6 cubic honeycomb, h{4,3,6} has alternating tetrahedral and hexagonal tiling cells with vertex figure is a quasiregular trihexagonal tiling, . Regular...

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

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

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

regular octahedron does, the octahedral symmetry O h {\displaystyle \mathrm {O} _{\mathrm {h} }} . A square and two hexagons surround each of its vertex...

different aperiodic tilings with 5-fold symmetry can be obtained by projecting two-dimensional slices of the honeycomb: the Penrose tiling composed of rhombi...

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...

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...

tiling honeycomb, ↔ Alternated order-4 hexagonal tiling honeycomb, ↔ Alternated order-5 hexagonal tiling honeycomb, ↔ Alternated order-6 hexagonal tiling honeycomb...

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

Each 24-cell in the 24-cell honeycomb has 24 neighboring 24-cells. With each neighbor it shares exactly one octahedral cell. It has 24 more neighbors...

Although it does not tile space by itself, it can tile space together with the regular tetrahedron to form the tetrahedral-octahedral honeycomb. It occurs in...

decomposed into square pyramids.) This honeycomb can be considered an elongated version of the tetrahedral-octahedral honeycomb. Critchlow, Keith. Order in Space:...