It can be realized as a projective polyhedron (a tessellation of the real projective plane by three quadrilaterals), which can be visualized by constructing the projective plane as a hemisphere where opposite points along the boundary are connected and dividing the hemisphere into three equal parts.

It has three square faces, six edges, and four vertices.

The hemicube should not be confused with the demicube – the hemicube is a projective polyhedron, while the demicube is an ordinary polyhedron (in Euclidean space).

The hemicube is the Petrie dual to the regular tetrahedron, with the four vertices, six edges of the tetrahedron, and three Petrie polygon quadrilateral faces.

The faces can be seen as red, green, and blue edge colorings in the tetrahedral graph: