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These models have been made in the 16-gon field. This small rhobicuboctahedron is an Archimedean solid, it is a convex polyhedron with eight triangular and eighteen square faces. It has 24 vertices with one triangle and three squares meeting at each.
The Johnson solid known as J37, The pseudo-rhobicuboctahedron (psi-rho or elongated square gyrobicupola) is not an Archimedean solid although it has the same combination of faces, one layer has been rotated so the end squares do not align making the triangles in two opposite layers offset from each other.