Pseudo-deltoidal icositetrahedron

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

Pseudo-deltoidal icositetrahedron
(see $3D$ model)
Type	Johnson dual, pseudo-uniform dual
Faces	$24$ , congruent
Face polygon	Kite with: $1$ obtuse angle $3$ equal acute angles
Edges	$24$ short + $24$ long = $48$
Vertices	$8$ of degree $3$ $18$ of degree $4$ $26$ in all
Vertex configurations	$4.4.4$ (for $8$ vertices) $4.4.4.4$ (for $2+8+8$ vertices)
Symmetry group	$D 4d = D 4v, [2 +,24], (2*4),$ order $4\times4$
Rotation group	$D 4, [2,4] +, (224),$ order $2\times4$
Dihedral angle	same value for short & long edges: $\arccos \left(-{\frac {7+4{\sqrt {2}}}{17}}\right)$ $\approx 138^{\circ }07'05''$
Properties	convex, regular vertices
Net	(click to enlarge)
Dual polyhedron	Elongated square gyrobicupola

As the pseudorhombicuboctahedron is tightly related to the rhombicuboctahedron, but has a twist along an equatorial belt of faces (and edges), the pseudo-deltoidal icositetrahedron is tightly related to the deltoidal icositetrahedron, but has a twist along an equator of (vertices and) edges.

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