Triangular-great rhombicosidodecahedral duoprism

The triangular-great rhombicosidodecahedral duoprism or tragrid is a convex uniform duoprism that consists of 3 great rhombicosidodecahedral prisms, 12 triangular-decagonal duoprisms, 20 triangular-hexagonal duoprisms and 30 triangular-square duoprisms. Each vertex joins 2 great rhombicosidodecahedral prisms, 1 triangular-square duoprism, 1 triangular-hexagonal duoprism, and 1 triangular-decagonal duoprism. It is a duoprism based on a triangle and a great rhombicosidodecahedron, which makes it a convex segmentoteron.

Vertex coordinates
The vertices of a triangular-great rhombicosidodecahedral duoprism of edge length 1 are given by all permutations of the last three coordinates of: along with all even permutations of the last three coordinates of:
 * $$\left(0,\,\frac{\sqrt3}3,\,±\frac12,\,±\frac12,\,±\frac{3+2\sqrt5}2\right),$$
 * $$\left(±\frac12,\,-\frac{\sqrt3}6,\,±\frac12,\,±\frac12,\,±\frac{3+2\sqrt5}2\right),$$
 * $$\left(0,\,\frac{\sqrt3}3,\,±\frac12,\,±\frac{2+\sqrt5}2,\,±\frac{4+\sqrt5}2\right),$$
 * $$\left(±\frac12,\,-\frac{\sqrt3}6,\,±\frac12,\,±\frac{2+\sqrt5}2,\,±\frac{4+\sqrt5}2\right),$$
 * $$\left(0,\,\frac{\sqrt3}3,\,±1,\,±\frac{3+\sqrt5}4,\,±\frac{7+3\sqrt5}4\right),$$
 * $$\left(±\frac12,\,-\frac{\sqrt3}6,\,±1,\,±\frac{3+\sqrt5}4,\,±\frac{7+3\sqrt5}4\right),$$
 * $$\left(0,\,\frac{\sqrt3}3,\,±\frac{3+\sqrt5}4,\,±3\frac{1+\sqrt5}4,\,±\frac{3+\sqrt5}2\right),$$
 * $$\left(±\frac12,\,-\frac{\sqrt3}6,\,±\frac{3+\sqrt5}4,\,±3\frac{1+\sqrt5}4,\,±\frac{3+\sqrt5}2\right),$$
 * $$\left(0,\,\frac{\sqrt3}3,\,±\frac{1+\sqrt5}2,\,±\frac{5+3\sqrt5}4,\,±\frac{5+\sqrt5}4\right),$$
 * $$\left(±\frac12,\,-\frac{\sqrt3}6,\,±\frac{1+\sqrt5}2,\,±\frac{5+3\sqrt5}4,\,±\frac{5+\sqrt5}4\right).$$