Related Polytopes and Honeycombs
It is similar to the cubic honeycomb {4,3,4} of Euclidean 3-space. Both have an octahedral vertex figure, replacing the cubic cells by dodecahedra.
There are fifteen uniform honeycombs in the Coxeter group family, including this regular form.
There are eleven uniform honeycombs in the bifurcating Coxeter group family, including this honeycomb in its alternated form. This construction can be represented by alternation (checkerboard) with two colors of dodecahedral cells.
There is another regular honeycomb in hyperbolic 3-space called the order-5 dodecahedral honeycomb which has 5 dodecahedra per edge.
This honeycomb is also related to the 120-cell which has 120 dodecahedra in 4-dimensional space, with 3 dodecahedra on each edge.
Read more about this topic: Order-4 Dodecahedral Honeycomb
Famous quotes containing the word related:
“The question of place and climate is most closely related to the question of nutrition. Nobody is free to live everywhere; and whoever has to solve great problems that challenge all his strength actually has a very restricted choice in this matter. The influence of climate on our metabolism, its retardation, its acceleration, goes so far that a mistaken choice of place and climate can not only estrange a man from his task but can actually keep it from him: he never gets to see it.”
—Friedrich Nietzsche (1844–1900)