Small biprismatorhombatodecachoron

The small biprismatorhombatodecachoron or sabipard is a convex isogonal polychoron that consists of 10 rhombitetratetrahedra, 30 rectangular trapezoprisms, 20 triangular prisms, 20 triangular antiprisms, and 60 wedges. 1 rhombitetratetrahedron, 2 rectangular trapezoprisms, 1 triangular prism, 1 triangular antiprism, and 3 wedges 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 prismatorhombated pentachora. In this case, if the prismatorhombated pentachora are of the form a3b3o3c, then c must be less than a+b/3 (producing the transitional biprismatorhombatodecachoron in the limiting case). This includes the convex hull of two uniform prismatorhombated pentachora. The lacing edges generally have length $$\sqrt{\frac{3a^2+2b^2+3c^2+2ab-6ac-2bc}{5}}$$.

Using the ratio method, the lowest possible ratio between the longest and shortest edges is 1:$$\frac{4+\sqrt{30}}{7}$$ ≈ 1:1.35389.