Coloring Uniform Honeycombs

Glenn Laigo, Ma. Louise Antonette N. De las Peñas and René Felix
Proceedings of Bridges 2009: Mathematics, Music, Art, Architecture, Culture (2009)
Pages 131–138 Regular Papers


In this paper, we discuss a method of arriving at colored three-dimensional uniform honeycombs. In particular, we present the construction of perfect and semi-perfect colorings of the truncated and bitruncated cubic honeycombs. If G is the symmetry group of an uncolored honeycomb, a coloring of the honeycomb is perfect if the group H consisting of elements that permute the colors of the given coloring is G. If H is such that [G:H] = 2, we say that the coloring of the honeycomb is semi-perfect.