order-4 dodecahedral honeycomb#Snub rectified order-4 dodecahedral honeycomb

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.

It has a half symmetry construction, {5,3^1,1}, with two types (colors) of dodecahedra in the Wythoff construction. {{CDD|node_1|5|node|3|node|4|node_h0}} ↔ {{CDD|node_1|5|node|split1|nodes}}.

File:H2-5-4-dual.svg, {5,4}]]

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A view of the order-4 dodecahedral honeycomb under the Beltrami-Klein model

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

{{Regular compact H3 honeycombs}}

There are fifteen uniform honeycombs in the [5,3,4] Coxeter group family, including this regular form.

{{534 family}}

There are eleven uniform honeycombs in the bifurcating [5,3^1,1] 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:

{{Octahedral_vertex_figure_tessellations}}

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

{{Dodecahedral_cell_tessellations}}