Transitional bicantitruncatodecachoron

The transitional bicantitruncatodecachoron or tabcated is a convex isogonal polychoron that consists of 10 truncated tetrahedra, 20 ditrigonal trapezoprisms, and 20 triangular trapezorhombihedra. 1 truncated tetrahedron, 2 ditrigonal trapezoprisms, and 2 triangular trapezorhombihedra join at each vertex.

It can also be formed as the convex hull of 2 oppositely oriented semi-uniform variants of the great rhombated pentachoron, where if the great rhombated pentachora are of the form a3b3c3o, then c = b+a/2. It is one of five polychora (including two transitional cases) formed from two great rhombated pentachora, and is the transitional point between the small bicantitruncatodecachoron and medial bicantitruncatodecachoron.

Using the ratio method, the lowest possible ratio between the longest and shortest edges is 1:$$\frac{2+\sqrt2}{2}$$ ≈ 1:1.70711.