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. 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.