In geometry, the tetrahemihexahedron is a nonconvex uniform polyhedron, indexed as U₄.

It contains the same 6 vertices as the regular octahedron.

It is the only nonprismatic uniform polyhedron with an odd number of faces. It is unique as the only uniform polyhedron with an Euler characteristic of 1 and is hence a representation of the real projective plane very similar to the Roman surface.

The "hemi" part of the name means some of the faces pass through the center of the polyhedron, in this case the square faces.

External links

• Mathworld
• VRML model: ^*
• Paper model

Uniform polyhedra | Quasiregular polyhedra | Polyhedral stellation | 四面半六面体