Elongated square gyrobicupola

Elongated square gyrobicupola
Elongated square gyrobicupola
Type	Canonical,; Johnson; J36 – J37 – J38
Faces	8 triangles; 18 squares
Edges	48
Vertices	24
Vertex configuration
Symmetry group
Properties	convex,; singular vertex figure
Net

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 was once mistakenly considered a rhombicuboctahedron by many mathematicians. 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. For this reason, it is also known as pseudo-rhombicuboctahedron, Miller solid,^[1] or Miller–Askinuze solid.^[2]

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[1]

[2]

Elongated square gyrobicupola

Type	Canonical, Johnson $J 36 - J 37 - J 38$
Faces	8 triangles 18 squares
Edges	48
Vertices	24
Vertex configuration	$8+16(3\cdot 4^{3})$
Symmetry group	$D_{4\mathrm {d} }$
Properties	convex, singular vertex figure
Net