Small bicantitruncatotetracontoctachoron

The small bicantitruncatotetracontoctachoron or sobcotic, also known as the runcinated tetracontoctachoron or runcinated bitetracontoctachoron, is a convex isogonal polychoron that consists of 48 truncated cubes, 144 ditetragonal trapezoprisms, 192 triangular prisms, 576 wedges, and 288 tetragonal disphenoids. 1 truncated cube, 2 ditetragonal 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 icositetrachora. In this case, if the great rhombated icositetrachora are of the form a3b4c3o, then c must be less than b+a/2 (producing the transitional bicantitruncatotetracontoctachoron in the limiting case). This includes the convex hull of two uniform great rhombated icositetrachora. The lacing edges generally have length $$\sqrt{(2-\sqrt2)a^2+(6-4\sqrt2)a(b-c)+(6-4\sqrt2)(b-c)^2}$$.

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

Using the ratio method, the lowest possible ratio between the longest and shortest edges is 1:$$\frac{18-3\sqrt2+\sqrt{410+266\sqrt2}}{34}$$ ≈ 1:1.22930.