The bitruncated cubic honeycomb is a space-filling tessellation (or honeycomb) in Euclidean 3-space made up of truncated octahedra.
It is one of 28 uniform honeycombs. It has 4 truncated octahedra around each vertex.
It can be realized as the Voronoi tessellation of the body-centred cubic lattice.
Being composed entirely of truncated octahedra, it is cell-transitive. It is also edge-transitive, with 2 hexagons and one square on each edge, and vertex-transitive.
Although a regular tetrahedron can not tessellate space alone, the dual of this honeycomb has identical tetrahedral cells with isosceles triangle faces (called a disphenoid tetrahedron) and these do tessellate space. The dual of this honeycomb is the disphenoid tetrahedral honeycomb.
Lord Kelvin conjectured that a variant of the bitruncated cubic honeycomb (with curved faces and edges, but the same combinatorial structure) is the optimal soap bubble foam. However, the Weaire–Phelan structure is a less symmetrical, but more efficient, foam of soap bubbles.
Famous quotes containing the word cubic:
“One of the great natural phenomena is the way in which a tube of toothpaste suddenly empties itself when it hears that you are planning a trip, so that when you come to pack it is just a twisted shell of its former self, with not even a cubic millimeter left to be squeezed out.”
—Robert Benchley (18891945)