Order-4 dodecahedral honeycomb
File:H3 534 CC center.png
Type
Hyperbolic regular honeycomb Uniform hyperbolic honeycomb
Schläfli symbol {5,3,4}1,1 }
Coxeter diagram File:CDel node 1.png File:CDel 5.png File:CDel node.png File:CDel 3.png File:CDel node.png File:CDel 4.png File:CDel node.png File:CDel node 1.png File:CDel 5.png File:CDel node.png File:CDel 3.png File:CDel node.png File:CDel 4.png File:CDel node h0.png File:CDel node 1.png File:CDel 5.png File:CDel node.png File:CDel split1.png File:CDel nodes.png
Cells
{5,3} (dodecahedron )File:Uniform polyhedron-53-t0.png
Faces
{5} (pentagon )
Edge figure {4} (square )
Vertex figure File:Order-4 dodecahedral honeycomb verf.png octahedron
Dual Order-5 cubic honeycomb
Coxeter group BH 3 , [4,3,5]DH 3 , [5,31,1 ]
Properties
Regular, Quasiregular honeycomb
In hyperbolic geometry , the order-4 dodecahedral honeycomb is one of four compact regular space-filling tessellations (or honeycombs ) of hyperbolic 3-space . With Schläfli symbol {5,3,4}, it has four dodecahedra around each edge , and 8 dodecahedra around each vertex in an octahedral arrangement. Its vertices are constructed from 3 orthogonal axes. Its dual is the order-5 cubic 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 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.
Description The dihedral angle of a regular dodecahedron is ~116.6°, so it is impossible to fit 4 of them on an edge in Euclidean 3-space. However in hyperbolic space a properly-scaled regular dodecahedron can be scaled so that its dihedral angles are reduced to 90 degrees, and then four fit exactly on every edge.
Symmetry It has a half symmetry construction, {5,31,1 }, with two types (colors) of dodecahedra in the Wythoff construction . File:CDel node 1.png File:CDel 5.png File:CDel node.png File:CDel 3.png File:CDel node.png File:CDel 4.png File:CDel node h0.png File:CDel node 1.png File:CDel 5.png File:CDel node.png File:CDel split1.png File:CDel nodes.png
Images File:H2-5-4-dual.svg It can be seen as analogous to the 2D hyperbolic order-4 pentagonal tiling , {5,4} File:Hyperbolic orthogonal dodecahedral honeycomb.png Beltrami-Klein model
Related polytopes and honeycombs There are four regular compact honeycombs in 3D hyperbolic space:
There are fifteen uniform honeycombs in the [5,3,4] Coxeter group family, including this regular form.
[5,3,4] family honeycombs
{5,3,4} File:CDel node 1.png File:CDel 5.png File:CDel node.png File:CDel 3.png File:CDel node.png File:CDel 4.png File:CDel node.png r{5,3,4} File:CDel node.png File:CDel 5.png File:CDel node 1.png File:CDel 3.png File:CDel node.png File:CDel 4.png File:CDel node.png t{5,3,4} File:CDel node 1.png File:CDel 5.png File:CDel node 1.png File:CDel 3.png File:CDel node.png File:CDel 4.png File:CDel node.png rr{5,3,4} File:CDel node 1.png File:CDel 5.png File:CDel node.png File:CDel 3.png File:CDel node 1.png File:CDel 4.png File:CDel node.png t0,3 {5,3,4} File:CDel node 1.png File:CDel 5.png File:CDel node.png File:CDel 3.png File:CDel node.png File:CDel 4.png File:CDel node 1.png tr{5,3,4} File:CDel node 1.png File:CDel 5.png File:CDel node 1.png File:CDel 3.png File:CDel node 1.png File:CDel 4.png File:CDel node.png t0,1,3 {5,3,4} File:CDel node 1.png File:CDel 5.png File:CDel node 1.png File:CDel 3.png File:CDel node.png File:CDel 4.png File:CDel node 1.png t0,1,2,3 {5,3,4} File:CDel node 1.png File:CDel 5.png File:CDel node 1.png File:CDel 3.png File:CDel node 1.png File:CDel 4.png File:CDel node 1.png
File:H3 534 CC center.png File:H3 534 CC center 0100.png File:H3 435-0011 center ultrawide.png File:H3 534-1010 center ultrawide.png File:H3 534-1001 center ultrawide.png File:H3 534-1110 center ultrawide.png File:H3 534-1101 center ultrawide.png File:H3 534-1111 center ultrawide.png
File:H3 435 CC center.png File:H3 435 CC center 0100.png File:H3 534-0011 center ultrawide.png File:H3 534-0101 center ultrawide.png File:H3 534-0110 center ultrawide.png File:H3 534-0111 center ultrawide.png File:H3 534-1011 center ultrawide.png
{4,3,5} File:CDel node 1.png File:CDel 4.png File:CDel node.png File:CDel 3.png File:CDel node.png File:CDel 5.png File:CDel node.png r{4,3,5} File:CDel node.png File:CDel 4.png File:CDel node 1.png File:CDel 3.png File:CDel node.png File:CDel 5.png File:CDel node.png t{4,3,5} File:CDel node 1.png File:CDel 4.png File:CDel node 1.png File:CDel 3.png File:CDel node.png File:CDel 5.png File:CDel node.png rr{4,3,5} File:CDel node 1.png File:CDel 4.png File:CDel node.png File:CDel 3.png File:CDel node 1.png File:CDel 5.png File:CDel node.png 2t{4,3,5} File:CDel node.png File:CDel 4.png File:CDel node 1.png File:CDel 3.png File:CDel node 1.png File:CDel 5.png File:CDel node.png tr{4,3,5} File:CDel node 1.png File:CDel 4.png File:CDel node 1.png File:CDel 3.png File:CDel node 1.png File:CDel 5.png File:CDel node.png t0,1,3 {4,3,5} File:CDel node 1.png File:CDel 4.png File:CDel node 1.png File:CDel 3.png File:CDel node.png File:CDel 5.png File:CDel node 1.png t0,1,2,3 {4,3,5} File:CDel node 1.png File:CDel 4.png File:CDel node 1.png File:CDel 3.png File:CDel node 1.png File:CDel 5.png File:CDel node 1.png
There are eleven uniform honeycombs in the bifurcating [5,31,1 ] Coxeter group family, including this honeycomb in its alternated form.
This construction can be represented by alternation (checkerboard) with two colors of dodecahedral cells.
This honeycomb is also related to the 16-cell , cubic honeycomb , and order-4 hexagonal tiling honeycomb all which have octahedral vertex figures:
{p,3,4} regular honeycombs
Space
S3
E3
H3
Form
Finite
Affine
Compact
Paracompact
Noncompact
Name
{3,3,4} File:CDel node 1.png File:CDel 3.png File:CDel node.png File:CDel 3.png File:CDel node.png File:CDel 4.png File:CDel node.png File:CDel node 1.png File:CDel 3.png File:CDel node.png File:CDel split1.png File:CDel nodes.png {4,3,4} File:CDel node 1.png File:CDel 4.png File:CDel node.png File:CDel 3.png File:CDel node.png File:CDel 4.png File:CDel node.png File:CDel node 1.png File:CDel 4.png File:CDel node.png File:CDel split1.png File:CDel nodes.png File:CDel labelinfin.png File:CDel branch 10.png File:CDel 2.png File:CDel labelinfin.png File:CDel branch 10.png File:CDel 2.png File:CDel labelinfin.png File:CDel branch 10.png File:CDel labelinfin.png File:CDel branch 11.png File:CDel 2.png File:CDel labelinfin.png File:CDel branch 11.png File:CDel 2.png File:CDel labelinfin.png File:CDel branch 11.png {5,3,4} File:CDel node 1.png File:CDel 5.png File:CDel node.png File:CDel 3.png File:CDel node.png File:CDel 4.png File:CDel node.png File:CDel node 1.png File:CDel 5.png File:CDel node.png File:CDel split1.png File:CDel nodes.png {6,3,4} File:CDel node 1.png File:CDel 6.png File:CDel node.png File:CDel 3.png File:CDel node.png File:CDel 4.png File:CDel node.png File:CDel node 1.png File:CDel 6.png File:CDel node.png File:CDel split1.png File:CDel nodes.png File:CDel node.png File:CDel ultra.png File:CDel node 1.png File:CDel split1.png File:CDel branch 11.png File:CDel uaub.png File:CDel nodes.png File:CDel node 1.png File:CDel ultra.png File:CDel node 1.png File:CDel split1.png File:CDel branch 11.png File:CDel uaub.png File:CDel nodes 11.png {7,3,4} File:CDel node 1.png File:CDel 7.png File:CDel node.png File:CDel 3.png File:CDel node.png File:CDel 4.png File:CDel node.png File:CDel node 1.png File:CDel 7.png File:CDel node.png File:CDel split1.png File:CDel nodes.png {8,3,4} File:CDel node 1.png File:CDel 8.png File:CDel node.png File:CDel 3.png File:CDel node.png File:CDel 4.png File:CDel node.png File:CDel node 1.png File:CDel 8.png File:CDel node.png File:CDel split1.png File:CDel nodes.png File:CDel node.png File:CDel ultra.png File:CDel node 1.png File:CDel split1-44.png File:CDel branch 11.png File:CDel label4.png File:CDel uaub.png File:CDel nodes.png File:CDel node 1.png File:CDel ultra.png File:CDel node 1.png File:CDel split1-44.png File:CDel branch 11.png File:CDel label4.png File:CDel uaub.png File:CDel nodes 11.png ... {∞,3,4} File:CDel node 1.png File:CDel infin.png File:CDel node.png File:CDel 3.png File:CDel node.png File:CDel 4.png File:CDel node.png File:CDel node 1.png File:CDel infin.png File:CDel node.png File:CDel split1.png File:CDel nodes.png File:CDel node.png File:CDel ultra.png File:CDel node 1.png File:CDel split1-ii.png File:CDel branch 11.png File:CDel labelinfin.png File:CDel uaub.png File:CDel nodes.png File:CDel node 1.png File:CDel ultra.png File:CDel node 1.png File:CDel split1-ii.png File:CDel branch 11.png File:CDel labelinfin.png File:CDel uaub.png File:CDel nodes 11.png
Image
File:Stereographic polytope 16cell.png File:Cubic honeycomb.png File:H3 534 CC center.png File:H3 634 FC boundary.png File:Hyperbolic honeycomb 7-3-4 poincare.png File:Hyperbolic honeycomb 8-3-4 poincare.png File:Hyperbolic honeycomb i-3-4 poincare.png
Cells
File:Tetrahedron.png {3,3} File:CDel node 1.png File:CDel 3.png File:CDel node.png File:CDel 3.png File:CDel node.png File:Hexahedron.png {4,3} File:CDel node 1.png File:CDel 4.png File:CDel node.png File:CDel 3.png File:CDel node.png File:Dodecahedron.png {5,3} File:CDel node 1.png File:CDel 5.png File:CDel node.png File:CDel 3.png File:CDel node.png File:Uniform tiling 63-t0.svg {6,3} File:CDel node 1.png File:CDel 6.png File:CDel node.png File:CDel 3.png File:CDel node.png File:Heptagonal tiling.svg {7,3} File:CDel node 1.png File:CDel 7.png File:CDel node.png File:CDel 3.png File:CDel node.png File:H2-8-3-dual.svg {8,3} File:CDel node 1.png File:CDel 8.png File:CDel node.png File:CDel 3.png File:CDel node.png File:H2-I-3-dual.svg {∞,3} File:CDel node 1.png File:CDel infin.png File:CDel node.png File:CDel 3.png File:CDel node.png
This honeycomb is a part of a sequence of polychora and honeycombs with dodecahedral cells:
{5,3,p}
Space
S3
H3
Form
Finite
Compact
Paracompact
Noncompact
Name
{5,3,3} File:CDel node 1.png File:CDel 5.png File:CDel node.png File:CDel 3.png File:CDel node.png File:CDel 3.png File:CDel node.png {5,3,4} File:CDel node 1.png File:CDel 5.png File:CDel node.png File:CDel 3.png File:CDel node.png File:CDel 4.png File:CDel node.png File:CDel node 1.png File:CDel 5.png File:CDel node.png File:CDel split1.png File:CDel nodes.png {5,3,5} File:CDel node 1.png File:CDel 5.png File:CDel node.png File:CDel 3.png File:CDel node.png File:CDel 5.png File:CDel node.png {5,3,6} File:CDel node 1.png File:CDel 5.png File:CDel node.png File:CDel 3.png File:CDel node.png File:CDel 6.png File:CDel node.png File:CDel node 1.png File:CDel 5.png File:CDel node.png File:CDel split1.png File:CDel branch.png {5,3,7} File:CDel node 1.png File:CDel 5.png File:CDel node.png File:CDel 3.png File:CDel node.png File:CDel 7.png File:CDel node.png {5,3,8} File:CDel node 1.png File:CDel 5.png File:CDel node.png File:CDel 3.png File:CDel node.png File:CDel 8.png File:CDel node.png File:CDel node 1.png File:CDel 5.png File:CDel node.png File:CDel split1.png File:CDel branch.png File:CDel label4.png ... {5,3,∞} File:CDel node 1.png File:CDel 5.png File:CDel node.png File:CDel 3.png File:CDel node.png File:CDel infin.png File:CDel node.png File:CDel node 1.png File:CDel 5.png File:CDel node.png File:CDel split1.png File:CDel branch.png File:CDel labelinfin.png
Image
File:Schlegel wireframe 120-cell.png File:H3 534 CC center.png File:H3 535 CC center.png File:H3 536 CC center.png File:Hyperbolic honeycomb 5-3-7 poincare.png File:Hyperbolic honeycomb 5-3-8 poincare.png File:Hyperbolic honeycomb 5-3-i poincare.png
VertexFile:CDel node 1.png File:CDel 3.png File:CDel node.png File:CDel p.png File:CDel node.png
File:Tetrahedron.png {3,3} File:CDel node 1.png File:CDel 3.png File:CDel node.png File:CDel 3.png File:CDel node.png File:Octahedron.png {3,4} File:CDel node 1.png File:CDel 3.png File:CDel node.png File:CDel 4.png File:CDel node.png File:Icosahedron.png {3,5} File:CDel node 1.png File:CDel 3.png File:CDel node.png File:CDel 5.png File:CDel node.png File:Uniform tiling 63-t2.svg {3,6} File:CDel node 1.png File:CDel 3.png File:CDel node.png File:CDel 6.png File:CDel node.png File:Order-7 triangular tiling.svg {3,7} File:CDel node 1.png File:CDel 3.png File:CDel node.png File:CDel 7.png File:CDel node.png File:H2-8-3-primal.svg {3,8} File:CDel node 1.png File:CDel 3.png File:CDel node.png File:CDel 8.png File:CDel node.png File:H2 tiling 23i-4.png {3,∞} File:CDel node 1.png File:CDel 3.png File:CDel node.png File:CDel infin.png File:CDel node.png
Rectified order-4 dodecahedral honeycomb
Rectified order-4 dodecahedral honeycomb
Type
Uniform honeycombs in hyperbolic space
Schläfli symbol r{5,3,4}1,1 }
Coxeter diagram File:CDel node.png File:CDel 5.png File:CDel node 1.png File:CDel 3.png File:CDel node.png File:CDel 4.png File:CDel node.png File:CDel node.png File:CDel 5.png File:CDel node 1.png File:CDel 3.png File:CDel node.png File:CDel 4.png File:CDel node h0.png File:CDel node.png File:CDel 5.png File:CDel node 1.png File:CDel split1.png File:CDel nodes.png
Cells
r{5,3} File:Uniform polyhedron-53-t1.png {3,4} File:Uniform polyhedron-43-t2.png
Faces
triangle {3}pentagon {5}
Vertex figure File:Rectified order-4 dodecahedral honeycomb verf.png square prism
Coxeter group B H ‾ 3 D H ‾ 3 1,1 ]
Properties
Vertex-transitive, edge-transitive
The rectified order-4 dodecahedral honeycomb , File:CDel node.png File:CDel 5.png File:CDel node 1.png File:CDel 3.png File:CDel node.png File:CDel 4.png File:CDel node.png octahedron and icosidodecahedron cells, with a square prism vertex figure .
File:H3 534 CC center 0100.png File:Rectified order 4 dodecahedral honeycomb.png File:H2-5-4-rectified.svg It can be seen as analogous to the 2D hyperbolic tetrapentagonal tiling , r{5,4} Related honeycombs There are four rectified compact regular honeycombs:
Truncated order-4 dodecahedral honeycomb
Truncated order-4 dodecahedral honeycomb
Type
Uniform honeycombs in hyperbolic space
Schläfli symbol t{5,3,4}1,1 }
Coxeter diagram File:CDel node 1.png File:CDel 5.png File:CDel node 1.png File:CDel 3.png File:CDel node.png File:CDel 4.png File:CDel node.png File:CDel node 1.png File:CDel 5.png File:CDel node 1.png File:CDel 3.png File:CDel node.png File:CDel 4.png File:CDel node h0.png File:CDel node 1.png File:CDel 5.png File:CDel node 1.png File:CDel split1.png File:CDel nodes.png
Cells
t{5,3} File:Uniform polyhedron-53-t01.png {3,4} File:Uniform polyhedron-43-t2.png
Faces
triangle {3}decagon {10}
Vertex figure File:Truncated order-4 dodecahedral honeycomb verf.png square pyramid
Coxeter group B H ‾ 3 D H ‾ 3 1,1 ]
Properties
Vertex-transitive
The truncated order-4 dodecahedral honeycomb , File:CDel node 1.png File:CDel 5.png File:CDel node 1.png File:CDel 3.png File:CDel node.png File:CDel 4.png File:CDel node.png octahedron and truncated dodecahedron cells, with a square pyramid vertex figure .
File:H3 435-0011 center ultrawide.png truncated order-4 pentagonal tiling , t{5,4} with truncated pentagon and square faces:
File:H2-5-4-trunc-dual.svg Related honeycombs
Bitruncated order-4 dodecahedral honeycomb
Bitruncated order-4 dodecahedral honeycomb
Type
Uniform honeycombs in hyperbolic space
Schläfli symbol 2t{5,3,4}1,1 }
Coxeter diagram File:CDel node.png File:CDel 5.png File:CDel node 1.png File:CDel 3.png File:CDel node 1.png File:CDel 4.png File:CDel node.png File:CDel node.png File:CDel 5.png File:CDel node 1.png File:CDel 3.png File:CDel node 1.png File:CDel 4.png File:CDel node h0.png File:CDel node.png File:CDel 5.png File:CDel node 1.png File:CDel split1.png File:CDel nodes 11.png
Cells
t{3,5} File:Uniform polyhedron-53-t12.png t{3,4} File:Uniform polyhedron-43-t12.png
Faces
square {4}pentagon {5}hexagon {6}
Vertex figure File:Bitruncated order-4 dodecahedral honeycomb verf.png digonal disphenoid
Coxeter group B H ‾ 3 D H ‾ 3 1,1 ]
Properties
Vertex-transitive
The bitruncated order-4 dodecahedral honeycomb , or bitruncated order-5 cubic honeycomb , File:CDel node.png File:CDel 5.png File:CDel node 1.png File:CDel 3.png File:CDel node 1.png File:CDel 4.png File:CDel node.png truncated octahedron and truncated icosahedron cells, with a digonal disphenoid vertex figure .
File:H3 534-0110 center ultrawide.png
Related honeycombs
Cantellated order-4 dodecahedral honeycomb
Cantellated order-4 dodecahedral honeycomb
Type
Uniform honeycombs in hyperbolic space
Schläfli symbol rr{5,3,4}1,1 }
Coxeter diagram File:CDel node 1.png File:CDel 5.png File:CDel node.png File:CDel 3.png File:CDel node 1.png File:CDel 4.png File:CDel node.png File:CDel node 1.png File:CDel 5.png File:CDel node.png File:CDel 3.png File:CDel node 1.png File:CDel 4.png File:CDel node h0.png File:CDel node 1.png File:CDel 5.png File:CDel node.png File:CDel split1.png File:CDel nodes 11.png
Cells
rr{3,5} File:Uniform polyhedron-53-t02.png r{3,4} File:Uniform polyhedron-43-t1.png {}x{4} File:Tetragonal prism.png
Faces
triangle {3}square {4}pentagon {5}
Vertex figure File:Cantellated order-4 dodecahedral honeycomb verf.png wedge
Coxeter group B H ‾ 3 D H ‾ 3 1,1 ]
Properties
Vertex-transitive
The cantellated order-4 dodecahedral honeycomb , File:CDel node 1.png File:CDel 5.png File:CDel node.png File:CDel 3.png File:CDel node 1.png File:CDel 4.png File:CDel node.png rhombicosidodecahedron , cuboctahedron , and cube cells, with a wedge vertex figure .
File:H3 534-1010 center ultrawide.png
Related honeycombs
Cantitruncated order-4 dodecahedral honeycomb
Cantitruncated order-4 dodecahedral honeycomb
Type
Uniform honeycombs in hyperbolic space
Schläfli symbol tr{5,3,4}1,1 }
Coxeter diagram File:CDel node 1.png File:CDel 5.png File:CDel node 1.png File:CDel 3.png File:CDel node 1.png File:CDel 4.png File:CDel node.png File:CDel node 1.png File:CDel 5.png File:CDel node 1.png File:CDel 3.png File:CDel node 1.png File:CDel 4.png File:CDel node h0.png File:CDel node 1.png File:CDel 5.png File:CDel node 1.png File:CDel split1.png File:CDel nodes 11.png
Cells
tr{3,5} File:Uniform polyhedron-53-t012.png t{3,4} File:Uniform polyhedron-43-t12.png {}x{4} File:Tetragonal prism.png
Faces
square {4}hexagon {6}decagon {10}
Vertex figure File:Cantitruncated order-4 dodecahedral honeycomb verf.png mirrored sphenoid
Coxeter group B H ‾ 3 D H ‾ 3 1,1 ]
Properties
Vertex-transitive
The cantitruncated order-4 dodecahedral honeycomb , File:CDel node 1.png File:CDel 5.png File:CDel node 1.png File:CDel 3.png File:CDel node 1.png File:CDel 4.png File:CDel node.png truncated icosidodecahedron , truncated octahedron , and cube cells, with a mirrored sphenoid vertex figure .
File:H3 534-1110 center ultrawide.png
Related honeycombs
Runcinated order-4 dodecahedral honeycomb The runcinated order-4 dodecahedral honeycomb is the same as the runcinated order-5 cubic honeycomb .
Runcitruncated order-4 dodecahedral honeycomb The runcitruncated order-4 dodecahedral honeycomb , File:CDel node 1.png File:CDel 5.png File:CDel node 1.png File:CDel 3.png File:CDel node.png File:CDel 4.png File:CDel node 1.png truncated dodecahedron , rhombicuboctahedron , decagonal prism , and cube cells, with an isosceles-trapezoidal pyramid vertex figure .
File:H3 534-1101 center ultrawide.png
Related honeycombs
Four runcitruncated regular compact honeycombs in H3
Image
File:H3 534-1101 center ultrawide.png File:H3 534-1011 center ultrawide.png File:H3 353-1101 center ultrawide.png File:H3 535-1101 center ultrawide.png
Symbols
t0,1,3 {5,3,4} File:CDel node 1.png File:CDel 5.png File:CDel node 1.png File:CDel 3.png File:CDel node.png File:CDel 4.png File:CDel node 1.png t0,1,3 {4,3,5} File:CDel node 1.png File:CDel 4.png File:CDel node 1.png File:CDel 3.png File:CDel node.png File:CDel 5.png File:CDel node 1.png t0,1,3 {3,5,3} File:CDel node 1.png File:CDel 3.png File:CDel node 1.png File:CDel 5.png File:CDel node.png File:CDel 3.png File:CDel node 1.png t0,1,3 {5,3,5} File:CDel node 1.png File:CDel 5.png File:CDel node 1.png File:CDel 3.png File:CDel node.png File:CDel 5.png File:CDel node 1.png
Vertex
File:Runcitruncated order-4 dodecahedral honeycomb verf.png File:Runcitruncated order-5 cubic honeycomb verf.png File:Runcitruncated icosahedral honeycomb verf.png File:Runcitruncated order-5 dodecahedral honeycomb verf.png
Runcicantellated order-4 dodecahedral honeycomb The runcicantellated order-4 dodecahedral honeycomb is the same as the runcitruncated order-5 cubic honeycomb .
Omnitruncated order-4 dodecahedral honeycomb The omnitruncated order-4 dodecahedral honeycomb is the same as the omnitruncated order-5 cubic honeycomb .
See also References Coxeter , Regular Polytopes ISBN 0-486-61480-8 . (Tables I and II: Regular polytopes and honeycombs, pp. 294–296)Coxeter , The Beauty of Geometry: Twelve Essays , Dover Publications, 1999 ISBN 0-486-40919-8 (Chapter 10: Regular honeycombs in hyperbolic space, Summary tables II, III, IV, V, p212-213)Jeffrey R. Weeks The Shape of Space, 2nd edition ISBN 0-8247-0709-5 (Chapter 16-17: Geometries on Three-manifolds I, II)Norman Johnson Uniform Polytopes , Manuscript
N.W. Johnson : The Theory of Uniform Polytopes and Honeycombs , Ph.D. Dissertation, University of Toronto, 1966N.W. Johnson: Geometries and Transformations , (2018) Chapter 13: Hyperbolic Coxeter groups
