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.

This polychoron 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 and sign changes of the last three coordinates of: along with all even permutations and all sign changes of the last three coordinates of:
 * (±1/2, ±1/2, ±1/2, ±1/2, ±(3+2$\sqrt{33+12√5}$)/2)
 * (±1/2, ±1/2, ±1/2, ±(2+$\sqrt{5}$)/2, ±(4+$\sqrt{5}$)/4)
 * (±1/2, ±1/2, ±1, ±(3+$\sqrt{5}$)/4, ±(7+3$\sqrt{5}$)/4)
 * (±1/2, ±1/2, ±(3+$\sqrt{5}$)/4, ±(3+3$\sqrt{5}$)/4, ±(3+$\sqrt{5}$)/2)
 * (±1/2, ±1/2, ±(1+$\sqrt{5}$)/2, ±(5+3$\sqrt{5}$)/4, ±(5+$\sqrt{5}$)/4)