Pseudo-deltoidal icositetrahedron

The pseudo-deltoidal icositetrahedron is a convex polyhedron with 24 kites as its faces. It is the dual of the pseudorhombicuboctahedron (also known as the elongated square gyrobicupola).

Pseudo-deltoidal icositetrahedron
TypeJohnson solid dual,
Pseudo-uniform polyhedron dual
Faces
24 kites
Edges48
Vertices26
Vertex configuration(2) 4.4.4
(8+8+2) 4.4.4.4
Symmetry groupDihedral (D4d)
Dual polyhedronElongated square gyrobicupola
Propertiesconvex
Net
(click to enlarge)

It is similar to the deltoidal icositetrahedron, but has a twist, similar to the relationship between the pseudorhombicuboctahedron and the rhombicuboctahedron. As the pseudorhombicuboctahedron is not truly vertex-transitive, the pseudo-deltoidal icositetrahedron is not truly face-transitive, with its faces in two different symmetry orbits (three if one only considers rotational symmetries); however, since the pseudorhombicuboctahedron has a singular vertex figure, the pseudo-deltoidal icositetrahedron has only one type of face (monohedral).

Pseudo- and actual deltoidal icositetrahedron
Pseudo- and actual rhombicuboctahedron
Pseudo- and actual deltoidal icositetrahedron
Pseudo- and actual great deltoidal icositetrahedron
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