order-5 dodecahedral honeycomb#Rectified order-5 dodecahedral honeycomb

The dihedral angle of a Euclidean regular dodecahedron is ~116.6°, so no more than three of them can fit around an edge in Euclidean 3-space. In hyperbolic space, however, the dihedral angle is smaller than it is in Euclidean space, and depends on the size of the figure; the smallest possible dihedral angle is 60°, for an ideal hyperbolic regular dodecahedron with infinitely long edges. The dodecahedra in this dodecahedral honeycomb are sized so that all of their dihedral angles are exactly 72°.

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There are four regular compact honeycombs in 3D hyperbolic space:

{{Regular compact H3 honeycombs}}

There is another honeycomb in hyperbolic 3-space called the order-4 dodecahedral honeycomb, {5,3,4}, which has only four dodecahedra per edge. These honeycombs are also related to the 120-cell which can be considered as a honeycomb in positively curved space (the surface of a 4-dimensional sphere), with three dodecahedra on each edge, {5,3,3}. Lastly the dodecahedral ditope, {5,3,2} exists on a 3-sphere, with 2 hemispherical cells.

There are nine uniform honeycombs in the [5,3,5] Coxeter group family, including this regular form. Also the bitruncated form, t_1,2{5,3,5}, {{CDD|node|5|node_1|3|node_1|5|node}}, of this honeycomb has all truncated icosahedron cells.

{{535 family}}

The Seifert–Weber space is a compact manifold that can be formed as a quotient space of the order-5 dodecahedral honeycomb.

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

{{Icosahedral vertex figure tessellations}}

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

{{Dodecahedral_tessellations small}}

{{Symmetric2_tessellations}}