The **quarter cubic honeycomb** (or **bitruncated alternated cubic honeycomb**) is a space-filling tessellation (or honeycomb) in Euclidean 3-space. It is composed of tetrahedra and truncated tetrahedra in a ratio of 1:1. It is called "quarter-cubic" because its symmetry unit – the minimal block from which the pattern is developed by reflections – consists of four such units of the cubic honeycomb.

It is vertex-transitive with 6 truncated tetrahedra and 2 tetrahedra around each vertex.

It is one of the 28 convex uniform honeycombs.

The faces of this honeycomb's cells form four families of parallel planes, each with a 3.6.3.6 tiling.

Its vertex figure is an isosceles antiprism: two equilateral triangles joined by six isosceles triangles.

Edge framework

Read more about Quarter Cubic Honeycomb: Symmetry

### Famous quotes containing the words quarter and/or cubic:

“I was able to believe for years that going to Madame Swann’s was a vague chimera that I would never attain; after having passed a *quarter* of an hour there, it was the time at which I did not know her which became to me a chimera and vague, as a possible destroyed by another possible.”

—Marcel Proust (1871–1922)

“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 (1889–1945)