Triakis triangular tegum

The triakis triangular tegum is a polyhedron formed from the triangular tegum by augmenting its faces with shallow triangular pyramids. It has 6 isosceles triangles and 12 scalene triangles as faces.

The canonical variant with midradius 1 has four edge lengths: one of length $$\frac{4\sqrt3}{9} ≈ 0.76980$$, one of length $$\frac{10\sqrt3}{9} ≈ 1.92450$$, one of length $$\frac{4\sqrt3}{3} ≈ 2.30940$$ and the other of length $$2\sqrt3 ≈ 3.46410$$.

Vertex coordinates
The vertices of a canonical triakis triangular tegum of midradius 1 are given by:
 * $$\left(0,\,0,\,±\frac{2\sqrt3}{3}\right),$$
 * $$\left(0,\,\frac23,\,±\frac{4\sqrt3}{9}\right),$$
 * $$\left(±\frac{\sqrt3}{3},\,-\frac13,\,±\frac{4\sqrt3}{9}\right),$$
 * $$\left(0,\,-2,\,0\right),$$
 * $$\left(±\sqrt3,\,1,\,0\right),$$

In vertex figures
A variant of the triakis triangular tegum with (A2×A1)+ symmetry occurs as the vertex figure of the tetrafold tetraswirlchoron.