Drilled Truncated Octahedron
This Demonstration shows a realization of Heawood's seven-color map using a toroid, each face of which is a regular polygon. The colored regions do not consist of a single face.
 L. Szilassi, "On Three Classes of Regular Toroids," Symmetry: Culture and Science, 11(1–4), 2000 pp. 317–335.  B. M. Stewart, Adventures among the Toroids, Okemos, Michigan: B. M. Stewart, rev. 2nd ed., 1980 p. 199.