Octahemioctahedron

In geometry, the octahemioctahedron or allelotetratetrahedron is a nonconvex uniform polyhedron, indexed as U3.

It is the only hemipolyhedron that is orientable, and the only uniform polyhedron with an Euler characteristic of zero (a topological torus).

[2] 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.

In practice the model prisms are cut off at a certain point that is convenient for the maker.

However, he also suggested that strictly speaking they are not polyhedra because their construction does not conform to the usual definitions.