# Monohedral Idemvalent Polyhedra that are Toroids

@article{Webber1997MonohedralIP, title={Monohedral Idemvalent Polyhedra that are Toroids}, author={W. Webber}, journal={Geometriae Dedicata}, year={1997}, volume={67}, pages={31-44} }

In this article we describe polyhedra of genus one that satisfy the following two properties: They have all faces congruent (monohedral) and they have the same number of faces at each vertex (idemvalent). In particular, the construction given yields polyhedra with six congruent triangles at each vertex. The construction given is a generalization of one given half a century ago by Alaoglu and Giese, and leads to many interesting toroidal polyhedra. We end by showing how the construction can… Expand

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