Small bicantitruncatodecachoron

The small bicantitruncatodecachoron or sobcated, also known as the runcinated decachoron or runcinated bidecachoron, is a convex isogonal polychoron that consists of 10 truncated tetrahedra, 20 ditrigonal trapezoprisms, 20 triangular prisms, 60 wedges, and 30 tetragonal disphenoids. 1 truncated tetrahedron, 2 ditrigonal trapezoprisms, 1 triangular prism, 3 wedges, and 1 tetragonal disphenoid join at each vertex.

It is one of a total of five distinct polychora (including two transitional cases) that can be obtained as the convex hull of two opposite great rhombated pentachora. In this case, if the great rhombated pentachora are of the form a3b3c3o, then c must be less than b+a/2 (producing the transitional bicantitruncatodecachoron in the limiting case). This includes the convex hull of two uniform great rhombated pentachora. The lacing edges generally have length $$\sqrt{\frac{3a^2+2b^2+2c^2+2ab-2ac-4bc}{5}}$$.

The cases where b = c (producing uniform truncated tetrahedral cells) can also be considered the result of expanding the cells of the decachoron or its dual bidecachoron outward and filling in the gaps.

Using the ratio method, the lowest possible ratio between the longest and shortest edges is 1:$$\frac{3+\sqrt{30}}{7}$$ ≈ 1:1.21103.