Type: Article

Realising equivelar toroids of type {4,4}

Bracho, Javie; Hubard, Isabel; Pellicer, Daniel;

Abstract:

By an equivelar toroid we understand a map satisfying the requirements of an abstract polyhedron on the 2-torus where all faces have a fixed number p of edges, and all vertices belong to a fixed number q of edges. We establish that if every regular toroid of type admits a faithful and symmetric realisation in a metric space then every equivelar toroid of type admits a faithful and symmetric realisation in . We exemplify this by showing that every equivelar toroid of type admits faithful and symmetric realisations in the 3-sphere and in 3-dimensional projective space.