Geodesic
A Generalization of the Regular Maps of Type{4, 4}b, c and {3, 6}b, c
Canadian mathematical bulletin, Tome 12 (1969) no. 3, pp. 293-297

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In [1], Coxeter gave a complete enumeration of the regular maps on a torus. The maps consist of two families of type {4, 4}b, c and {3, 6}b, c (and their duals). b and c are non-negative integers, which determine the maps uniquely. The maps are irreflexible if and only if bc(b - c) ≠ 0.On surfaces of genus h > 1, irreflexible regular maps are rather exceptional. The simplest surface of negative characteristic which admits irreflexible regular maps is the orientable surface of genus 7. This was shown by the author [4, Theorem 3. 1 ]. The corresponding map was discovered by J. R. Edmonds [2, p. 388]. 
Garbe, Dietmar. A Generalization of the Regular Maps of Type{4, 4}b, c and {3, 6}b, c. Canadian mathematical bulletin, Tome 12 (1969) no. 3, pp. 293-297. doi: 10.4153/CMB-1969-037-6
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     title = {A {Generalization} of the {Regular} {Maps} of {Type{4,} 4}b, c and {3, 6}b, c},
     journal = {Canadian mathematical bulletin},
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     year = {1969},
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     doi = {10.4153/CMB-1969-037-6},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/CMB-1969-037-6/}
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