Biprismatocubic honeycomb

The biprismatocubic honeycomb or bipach is an isogonal honeycomb that consists of cubes, square prisms, and rectangular trapezoprisms. 1 cube, 3 square prisms, and 6 rectangular trapezoprisms join at each vertex. It can be obtained as the union of two small prismated cubic honeycombs (that is, variants of the cubic honeycomb of the form x4o3o4y).

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

Using the ratio method, the lowest possible ratio between the longest and shortest edges is 1:$$\frac{3+2\sqrt3}{3}$$ ≈ 1:2.15470. This variants uses isosceles trapezoids with three edges of the same length.