Bidodecateron

The bidodecateron or bidot, also known as the triangular-duotegmatic icosateron or triangular duotegmatic alterprism, is a convex noble polyteron with 20 identical triangular duotegums as facets. 10 facets join at each vertex, with the vertex figure being a joined pentachoron. It can be obtained as the convex hull of a hexateron and its central inversion (or, equivalently, its dual). It is also the triangular member of an infinite series of isogonal duotegmatic alterprisms.

The ratio between the longest and shortest edges is 1:$$\frac{\sqrt6}{2}$$ ≈ 1:1.22474.

Vertex coordinates
The vertices of a bidodecateron, based on two hexatera of edge length 1, centered at the origin, are given by:
 * $$±\left(±\frac{1}{2},\,-\frac{\sqrt{3}}{6},\,-\frac{\sqrt{6}}{12},\,-\frac{\sqrt{10}}{20},\,-\frac{\sqrt{15}}{30}\right),$$
 * $$±\left(0,\,\frac{\sqrt{3}}{3},\,-\frac{\sqrt{6}}{12},\,-\frac{\sqrt{10}}{20},\,-\frac{\sqrt{15}}{30}\right),$$
 * $$±\left(0,\,0,\,\frac{\sqrt{6}}{4},\,-\frac{\sqrt{10}}{20},\,-\frac{\sqrt{15}}{30}\right),$$
 * $$±\left(0,\,0,\,0,\,\frac{\sqrt{10}}{5},\,-\frac{\sqrt{15}}{30}\right),$$
 * $$\left(0,\,0,\,0,\,0,\,±\frac{\sqrt{15}}{6}\right).$$