Small biprismatorhombatotetracontoctachoron

The small biprismatorhombatotetracontoctachoron or sabiparc is a convex isogonal polychoron that consists of 48 small rhombicuboctahedra, 144 square antiprisms, 288 rectangular trapezoprisms, 192 triangular prisms, and 576 wedges. 1 small rhombicuboctahedron, 1 square antiprism, 2 rectangular trapezoprisms, 1 triangular prism, 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 icositetrachora. In this case, if the prismatorhombated icositetrachora are of the form a3b4o3c, then c must be less than $$a+\frac{2-\sqrt2}{2}b$$ (producing the transitional biprismatorhombatotetracontoctachoron in the limiting case). This includes the convex hull of two uniform prismatorhombated icositetrachora. The lacing edges generally have length $$\sqrt{(6-4\sqrt2)b^2+(6-4\sqrt2)a(b-c)+(6-4\sqrt2)(b-c)^2+(2-\sqrt2)(a-c)^2}$$.

Using the ratio method, the lowest possible ratio between the longest and shortest edges is 1:$$\frac{38+3\sqrt2+\sqrt{842+786\sqrt2}}{62}$$ ≈ 1:1.39422.