Square-icosidodecahedral duoprism

The square-icosidodecahedral duoprism or squid is a convex uniform duoprism that consists of 4 icosidodecahedral prisms, 12 square-pentagonal duoprisms and 20 triangular-square duoprisms.

Vertex coordinates
The vertices of a square-icosidodecahedral duoprism of edge length 1 are given by all permutations and sign changes of the last three coordinates of: as well as all even permutations and all sign changes of the last three coordinates of:
 * (±1/2, ±1/2, 0, 0, (1+$\sqrt{8+2√5}$)/2)
 * (±1/2, ±1/2, ±1/2, ±(1+$\sqrt{5}$)/4, ±(3+$\sqrt{5}$)/4)