Tetrahedral transitional biomnitruncatodecachoron

The tetrahedral transitional biomnitruncatodecachoron or tetbotid is a convex isogonal polychoron that consists of 10 orthoaligned ditruncated tetrahedra, 20 ditrigonal prisms, and 30 rectangular trapezoprisms. 2 orthoaligned ditruncated tetrahedra, 1 ditrigonal prism, and 1 rectangular trapezoprism join at each vertex.

It is one of a total of four distinct polychora (including two transitional cases) that can be obtained as the convex hull of two opposite great disprismatopentapentachora (that is, variants of the great prismatodecachoron with single A4 symmetry). If the great disprismatopentapentachora are of the form a3b3c3d, then this form occurs when the great rhombitetratetrahedra a3b3c and b3c3d have the same circumradius, which happens if d = a+b/3-c/3. The lacing edges generally have length $$\sqrt{\frac{3(a-d)^2+2(b-c)^2+2(a-d)(b-c)}{5}}$$.

This polychoron can be alternated into a tetrahedral transitional omnisnub bidecachoron, which is also nonuniform.

Using the ratio method, the lowest possible ratio between the longest and shortest edges is 1:$$\frac{3+\sqrt3}{3}$$ ≈ 1:1.57735.