Bidiminished octahedron atop cuboctahedron

The bidiminished octahedron atop cuboctahedron or square atop cuboctahedron is a CRF segmentochoron (designated K-4.28 on Richard Klitzing's list). It consists of a square and a cuboctahedron as bases, connected by 2 cubes and 12 square pyramids. It can be formed by diminishing two vertices of the octahedron atop cuboctahedron segmentochoron.

Two square atop cuboctahedron segmentochora can be attached at their cuboctahedral bases to form the cyclotetradiminished icositetrachoron.