Small triambic icosahedron

The small triambic icosahedron, or stai, is a uniform dual polyhedron. It consists of 20 irregular hexagons, more specifically equilateral triambuses.

If its dual, the small ditrigonary icosidodecahedron, has an edge length of 1, then the edges of the hexagons will measure $$\frac{3\sqrt{10}-5\sqrt2}{5} ≈ 0.48315$$. The hexagons have alternating interior angles of $$\arccos\left(-\frac14\right) ≈ 104.47751°$$, and $$\arccos\left(\frac14\right)+60° ≈ 135.52249°$$.

Vertex coordinates
A small triambic icosahedron with dual edge length 1 has vertex coordinates given by all even permutations of:
 * $$\left(±\frac{5-\sqrt5}{10},\,±\frac{5+\sqrt5}{10},\,0\right),$$
 * $$\left(±\frac{\sqrt5-1}{2},\,±\frac{3-\sqrt5}{2},\,0\right),$$
 * $$\left(±\frac{\sqrt5}{5},\,±\frac{\sqrt5}{5},\,±\frac{\sqrt5}{5}\right).$$