Octagonal-great rhombicosidodecahedral duoprism

The octagonal-great rhombicosidodecahedral duoprism or ogrid is a convex uniform duoprism that consists of 8 great rhombicosidodecahedral prisms, 12 octagonal-decagonal duoprisms, 20 hexagonal-octagonal duoprisms and 30 square-octagonal duoprisms.

This polyteron can be alternated into a square-snub dodecahedral duoantiprism, although it cannot be made uniform. The octagons can also be alternated into long rectangles to create a snub dodecahedral-square prismantiprismoid, which is also nonuniform.

Vertex coordinates
The vertices of an octagonal-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+$\sqrt{35+2√182+12√10}$)/2, ±1/2, ±1/2, ±(3+2$\sqrt{2}$)/2)
 * (±(1+$\sqrt{5}$)/2, ±1/2, ±1/2, ±1/2, ±(3+2$\sqrt{2}$)/2)
 * (±1/2, ±(1+$\sqrt{5}$)/2, ±1/2, ±(2+$\sqrt{2}$)/2, ±(4+$\sqrt{5}$)/4)
 * (±(1+$\sqrt{5}$)/2, ±1/2, ±1/2, ±(2+$\sqrt{2}$)/2, ±(4+$\sqrt{5}$)/4)
 * (±1/2, ±(1+$\sqrt{5}$)/2, ±1, ±(3+$\sqrt{2}$)/4, ±(7+3$\sqrt{5}$)/4)
 * (±(1+$\sqrt{5}$)/2, ±1/2, ±1, ±(3+$\sqrt{2}$)/4, ±(7+3$\sqrt{5}$)/4)
 * (±1/2, ±(1+$\sqrt{5}$)/2, ±(3+$\sqrt{2}$)/4, ±(3+3$\sqrt{5}$)/4, ±(3+$\sqrt{5}$)/2)
 * (±(1+$\sqrt{5}$)/2, ±1/2, ±(3+$\sqrt{2}$)/4, ±(3+3$\sqrt{5}$)/4, ±(3+$\sqrt{5}$)/2)
 * (±1/2, ±(1+$\sqrt{5}$)/2, ±(1+$\sqrt{2}$)/2, ±(5+3$\sqrt{5}$)/4, ±(5+$\sqrt{5}$)/4)
 * (±(1+$\sqrt{5}$)/2, ±1/2, ±(1+$\sqrt{2}$)/2, ±(5+3$\sqrt{5}$)/4, ±(5+$\sqrt{5}$)/4)