Great triambic icosahedron

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

It appears the same as the medial triambic icosahedron.

If its dual, the great ditrigonary icosidodecahedron, has an edge length of 1, then the edges of the hexagons will measure $$\frac{5\sqrt2+3\sqrt{10}}{5} ≈ 3.31158$$. ​The hexagons have alternating interior angles of $$\arccos\left(\frac14\right)-60° ≈ 15.52249°$$, and $$\arccos\left(-\frac14\right) ≈ 104.47751°$$.

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