Elongated square gyrobicupola

In geometry, the elongated square gyrobicupola is a polyhedron constructed by two square cupolas attaching onto the bases of octagonal prism, with one of them rotated. It is also known as pseudo-rhombicuboctahedron because many mathematicians mistakenly constructed a rhombicuboctahedron. It is not considered to be an Archimedean solid because it lacks a set of global symmetries that map every vertex to every other vertex, unlike the 13 Archimedean solids. It is also a canonical polyhedron.

Elongated square gyrobicupola
Type	Canonical, Johnson J36 – J37 – J38
Faces	8 triangles 18 squares
Edges	48
Vertices	24
Vertex configuration	${\displaystyle 8+16(3\cdot 4^{3})}$
Symmetry group	${\displaystyle D_{4\mathrm {d} }}$
Dual polyhedron	Pseudo-deltoidal icositetrahedron
Properties	convex, singular vertex figure
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