hyperbolic 3-space, the order-infinite-3 triangular honeycomb (or 3,∞,3 honeycomb) is a regular space-filling tessellation (or honeycomb) with Schläfli...

geometry of hyperbolic 3-space, the order-7-3 triangular honeycomb (or 3,7,3 honeycomb) is a regular space-filling tessellation (or honeycomb) with Schläfli symbol...

geometry of hyperbolic 3-space, the order-8-3 triangular honeycomb (or 3,8,3 honeycomb) is a regular space-filling tessellation (or honeycomb) with Schläfli symbol...

vertex in an infinite-order triangular tiling vertex arrangement. It has a second construction as a uniform honeycomb, Schläfli symbol {3,(3,∞,3)}, Coxeter...

Wikimedia Commons has media related to Infinite-order triangular tiling. Infinite-order tetrahedral honeycomb List of regular polytopes List of uniform...

of hyperbolic geometry, the hexagonal tiling honeycomb is one of 11 regular paracompact honeycombs in 3-dimensional hyperbolic space. It is paracompact...

1+] ↔ [3,((3,3,3))], or [3,3[3]]: ↔ . The order-6 tetrahedral honeycomb is analogous to the two-dimensional infinite-order triangular tiling, {3,∞}. Both...

geometry of hyperbolic 3-space, the order-3-6 heptagonal honeycomb a regular space-filling tessellation (or honeycomb). Each infinite cell consists of a heptagonal...

The triangular tiling honeycomb is one of 11 paracompact regular space-filling tessellations (or honeycombs) in hyperbolic 3-space. It is called paracompact...

to the truncated infinite-order triangular tiling, : The order-4 hexagonal tiling honeycomb is a regular hyperbolic honeycomb in 3-space, and one of...

surrounding each edge of the honeycomb. Each vertex is ideal, and surrounded by infinitely many dodecahedra. The honeycomb has a triangular tiling vertex figure...

field of hyperbolic geometry, the order-5 hexagonal tiling honeycomb arises as one of 11 regular paracompact honeycombs in 3-dimensional hyperbolic space....

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

the geometry of hyperbolic 3-space, the order-6-4 triangular honeycomb is a regular space-filling tessellation (or honeycomb) with Schläfli symbol {3,6...

the geometry of hyperbolic 3-space, the order-7 dodecahedral honeycomb is a regular space-filling tessellation (or honeycomb). With Schläfli symbol {5...

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

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

Coxeter diagrams for each family. These families can produce uniform honeycombs with infinite or unbounded facets or vertex figure, including ideal vertices...

consisting of small rhombicuboctahedra , infinite order-8 triangular tilings , and infinite order-8 square tilings . The order-8 square tilings already intersect...

The order-4 octahedral honeycomb is a regular paracompact honeycomb in hyperbolic 3-space. It is paracompact because it has infinite vertex figures, with...

hyperbolic honeycombs. Any finite uniform polytope can be projected to its circumsphere to form a uniform honeycomb in spherical space. There are infinitely many...

the faces are infinite polygons (a bit like the apeirogonal hosohedron's digon faces, having a width larger than zero, are infinite stripes). Dihedra...

the geometry of hyperbolic 3-space, the order-4 icosahedral honeycomb is a regular space-filling tessellation (or honeycomb) with Schläfli symbol {3,5...

Schläfli symbol of the triangular tiling is {3,6}, the vertex figure of this honeycomb is a triangular tiling. Thus, infinitely many hexagonal tilings...

triangular hosohedral honeycomb Hexagonal hosohedral honeycomb[citation needed] Order-2 square tiling honeycomb Order-2 triangular tiling honeycomb Order-2...

an order-7 triangular tiling vertex figure. It a part of a sequence of regular polychora and honeycombs {p,3,p}: In the geometry of hyperbolic 3-space...

gyration operations. The total unique honeycombs above are 18. The prismatic stacks from infinite Coxeter groups for 3-space are: The C ~ 2 {\displaystyle...

together with the regular tetrahedron to form the tetrahedral-octahedral honeycomb. It occurs in nature in certain crystals, in architecture as part of certain...

{\displaystyle N_{2}={\frac {4n}{2\times 2+2n-2n}}=n,} and admits a new infinite class of regular polyhedra, which are the hosohedra. On a spherical surface...

geometry, the order-5 dodecahedral honeycomb is one of four compact regular space-filling tessellations (or honeycombs) in hyperbolic 3-space. With Schläfli...