Order-6 dodecahedral honeycomb

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Order-6 dodecahedral honeycomb

Perspective projection view
within Poincaré disk model
TypeHyperbolic regular honeycomb
Paracompact uniform honeycomb
Schläfli symbol{5,3,6}
{5,3[3]}
Coxeter diagram
=
Cellsdodecahedron {5,3}
Facespentagon {5}
Edge figurehexagon {6}
Vertex figure{3,6}
DualOrder-5 hexagonal tiling honeycomb
Coxeter groupHV3, [5,3,6]
HP3, [5,3[3]]
PropertiesRegular

The order-6 dodecahedral honeycomb a space-filling tessellations (or honeycombs) in hyperbolic 3-space. It has Schläfli symbol {5,3,6}, being composed of dodecahedral cells, each edge of the honeycomb is surrounded by six dodecahedra. Each vertex is ideal and surrounded by infinitely many dodecahedra with a vertex figure as a triangular tiling.

Symmetry

A half symmetry construction exists as with alternately colored dodecahedral cells.

Images


The model is cell-centered in the within Poincaré disk model, with the viewpoint then placed at the origin.

Related polytopes and honeycombs

It is one of 15 regular hyperbolic honeycombs in 3-space, 11 of which like this one are paracompact, with infinite cells or vertex figures.

There are 15 uniform honeycombs in the [5,3,6] Coxeter group family, including this regular form and its regular dual, order-5 hexagonal tiling honeycomb, {6,3,5}.

This honeycomb is a part of a sequence of polychora and honeycombs with triangular tiling vertex figures:

{p,3,6}
Space H3
Name {3,3,6}
 {4,3,6}
 {5,3,6}
 {6,3,6}
Image
Cells
{3,3}
{4,3}
{5,3}
{6,3}

This honeycomb is a part of a sequence of polychora and honeycombs with dodecahedral cells:

{5,3,p}
Space S3 H3
Name {5,3,3}
 {5,3,4}
 {5,3,5}
 {5,3,6}
Image
Vertex
figure
{3,3}
{3,4}
{3,5}
{3,6}

See also

References

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