Great birhombitetrahedral honeycomb

The great birhombitetrahedral honeycomb or gabreth is an isogonal honeycomb that consists of great rhombitetratetrahedra, ditrigonal trapezoprisms, and rectangular trapezoprisms. 2 of each type of cell join at each vertex. It can be obtained as a subsymmetrical faceting of the great prismated cubic honeycomb, by alternating its hexagons. However, it cannot be made uniform.

Using the ratio method, the lowest possible ratio between the longest and shortest edges is 1:2.

This honeycomb can be alternated into a snub bitetrahedral honeycomb, although it cannot be made uniform.