Biambodecachoron

The biambodecachoron or antiprismatodecachoron, short name bamid or apid, is a convex isogonal polychoron that consists of 10 tetrahedra and 20 triangular antiprisms. 2 tetrahedra and 6 triangular antiprisms join at each vertex. It can be obtained as the convex hull of two oppositely oriented rectified pentachora. Alternatively it can be obtained as the hull of the centers of the triangular faces of the decachoron.

It is also one of a number of polychora obtained as the hull of 2 10-3 step prisms.

The ratio between the longest and shortest edges is 1:$$\frac{\sqrt{10}}{2}$$ ≈ 1:1.58114.

Vertex coordinates
Coordinates for the vertices of a biambodecachoron, based on two rectified pentachora of edge length 1, centered at the origin, are given by:
 * $$±\left(-\frac{3\sqrt{10}}{20},\,-\frac{\sqrt6}{4},\,0,\,0\right),$$
 * $$±\left(-\frac{3\sqrt{10}}{20},\,\frac{\sqrt6}{12},\,-\frac{\sqrt3}{3},\,0\right),$$
 * $$±\left(-\frac{3\sqrt{10}}{20},\,\frac{\sqrt6}{12},\,\frac{\sqrt3}{6},\,±\frac12\right),$$
 * $$±\left(\frac{\sqrt{10}}{10},\,\frac{\sqrt6}{6},\,\frac{\sqrt3}{3},\,0\right),$$
 * $$±\left(\frac{\sqrt{10}}{10},\,-\frac{\sqrt6}{6},\,-\frac{\sqrt3}{3},\,0\right),$$
 * $$±\left(\frac{\sqrt{10}}{10},\,\frac{\sqrt6}{6},\,-\frac{\sqrt3}{6},\,±\frac12\right),$$
 * $$±\left(\frac{\sqrt{10}}{10},\,-\frac{\sqrt6}{6},\,\frac{\sqrt3}{6},\,±\frac12\right).$$