Small biomnitruncatodecachoron

The small biomnitruncatodecachoron or sabotid is a convex isogonal polychoron that consists of 10 great rhombitetratetrahedra, 20 ditrigonal prisms, 20 ditrigonal trapezoprisms, 30 rectangular trapezoprisms, and 60 rectangular frustums. 2 rectangular frustums and 1 of each of the other 4 cell types 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 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 small omnisnub bidecachoron, which is also nonuniform.

Using the ratio method, the lowest possible ratio between the longest and shortest edges is 1:$$\frac{7+\sqrt{35}}{7}$$ ≈ 1:1.84515.