Biscribed Non-Chiral Solids

For these pages, a biscribed solid is defined to be any convex polyhedron that has concentric circumscribed and inscribed spheres, where the sphere center is also the centroid of the vertices and the centroid of the face tangency points. The five Platonic solids are biscribed solids, but none of the Archimedean or Catalan solids are. The convexity criterion rules out the rest of the uniform polyhedra.