Medial triambic icosahedron

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

It appears the same as the great triambic icosahedron.

If its dual, the ditrigonary dodecadodecahedron, has an edge length of 1, then the edges of the hexagons will measure $$2\sqrt2 ≈ 2.82843$$. ​The hexagons have alternating interior angles of $$\arccos\left(\frac14\right)-60° ≈ 15.52249°$$, and $$\arccos\left(-\frac14\right)+120° ≈ 224.47751°$$.

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