Square-great rhombicosidodecahedral duoprism

The square-great rhombicosidodecahedral duoprism or squagrid is a convex uniform duoprism that consists of 4 great rhombicosidodecahedral prisms, 12 square-decagonal duoprisms, 20 square-hexagonal duoprisms and 30 tesseracts. Each vertex joins 2 great rhombicosidodecahedral prisms, 1 tesseract, 1 square-hexagonal duoprism, and 1 square-decagonal duoprism. It is a duoprism based on a square and a great rhombicosidodecahedron, which makes it a convex segmentoteron.

This polyteron can be alternated into a digonal-snub dodecahedral duoantiprism, although it cannot be made uniform.

Vertex coordinates
The vertices of a square-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:
 * $$\left(±\frac12,\,±\frac12,\,±\frac12,\,±\frac12,\,±\frac{3+2\sqrt5}2\right),$$
 * $$\left(±\frac12,\,±\frac12,\,±\frac12,\,±\frac{2+\sqrt5}2,\,±\frac{4+\sqrt5}2\right),$$
 * $$\left(±\frac12,\,±\frac12,\,±1,\,±\frac{3+\sqrt5}4,\,±\frac{7+3\sqrt5}4\right),$$
 * $$\left(±\frac12,\,±\frac12,\,±\frac{3+\sqrt5}4,\,±3\frac{1+\sqrt5}4,\,±\frac{3+\sqrt5}2\right),$$
 * $$\left(±\frac12,\,±\frac12,\,±\frac{1+\sqrt5}2,\,±\frac{5+3\sqrt5}4,\,±\frac{5+\sqrt5}4\right).$$

Representations
A triangular-great rhombicosidodecahedral duoprism has the following Coxeter diagrams:
 * x4o x5x3x (full symmetry)
 * x x x5x3x (great rhombicosidodecahedral prismatic prism)