Cantic snub cubic honeycomb

The cantic snub cubic honeycomb or casch is an isogonal honeycomb that consists of pyritosnub cubes, pyritohedral icosahedra, and wedges. 2 pyritosnub cubes, 1 pyrtohedral icosahedron, and 3 wedges join at each vertex. It can be obtained as a subsymmetrical faceting and alternation of the great rhombated cubic honeycomb, alternating the octagons into long rectangles. However, it cannot be made uniform.

Using the ratio method, the lowest possible ratio between the longest and shortest edges is 1:$$\frac{1+\sqrt5}{2}$$ ≈ 1:1.61803.