Tetrahemihexahedron

Its Wythoff symbol is 3/2 3 | 2, but that represents a double covering of the tetrahemihexahedron with eight triangles and six squares, paired and coinciding in space.

The three square faces of the tetrahemihexahedron are, like the three facial orientations of the cube, mutually perpendicular.

The "half-as-many" characteristic also means that hemi faces must pass through the center of the polyhedron, where they all intersect each other.

The tetrahemihexahedron is 2-covered by the cuboctahedron,[2] which accordingly has the same abstract vertex figure (2 triangles and two squares: 3.4.3.4) and twice the vertices, edges, and faces.

[4] In Magnus Wenninger's Dual Models, they are represented with intersecting prisms, each extending in both directions to the same vertex at infinity, in order to maintain symmetry.

The other four vertices exist at alternate corners of a central cube (a demicube, in this case a tetrahedron).