Monohedral idemvalent polyhedra that are toroids (Q1366278)

The author describes polyhedra of genus one that have all faces congruent (monohedral) and have the same number of faces at each vertex (idemvalent). The polyhedra obtained have six congruent triangles at each vertex. The building blocks are isohedral octahedra. The angle formed by opposite faces of such an octahedron is calculated, and if this angle is \({\pi\over n}\) a toroidal polyhedron can be obtained by reflecting the original octahedron in these face planes. It is formed by the \(2n\) reflection images of the original octahedron.