Geodesic
A Family of Regular Maps of Type {6, 6}
Canadian mathematical bulletin, Tome 5 (1962) no. 1, pp. 13-20

Voir la notice de l'article provenant de la source Cambridge University Press

In (4), pp. 25−27, Coxeter divided the regular maps on a surface of genus 1 into three infinite families. They are: (i) Maps of type {4, 4}. (ii) Maps of type {6, 3}. (iii) Maps of type {3, 6} (the duals of (ii)). We consider the family (iii). By adjoining an element to the group of any map in (iii) we shall derive the group of a regular map of type {6, 6}. Thus we produce a 1−1 correspondence between the members of the family (iii) and of the new family. Corresponding members in the two families have certain properties in common, the most interesting of which is the property of reflexibility. Our results are summarized in Theorems 1 and 2. 
Sherk, F.A. A Family of Regular Maps of Type {6, 6}. Canadian mathematical bulletin, Tome 5 (1962) no. 1, pp. 13-20. doi: 10.4153/CMB-1962-003-7
@article{10_4153_CMB_1962_003_7,
     author = {Sherk, F.A.},
     title = {A {Family} of {Regular} {Maps} of {Type} {6, 6}},
     journal = {Canadian mathematical bulletin},
     pages = {13--20},
     year = {1962},
     volume = {5},
     number = {1},
     doi = {10.4153/CMB-1962-003-7},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/CMB-1962-003-7/}
}
TY  - JOUR
AU  - Sherk, F.A.
TI  - A Family of Regular Maps of Type {6, 6}
JO  - Canadian mathematical bulletin
PY  - 1962
SP  - 13
EP  - 20
VL  - 5
IS  - 1
UR  - http://geodesic.mathdoc.fr/articles/10.4153/CMB-1962-003-7/
DO  - 10.4153/CMB-1962-003-7
ID  - 10_4153_CMB_1962_003_7
ER  - 
%0 Journal Article
%A Sherk, F.A.
%T A Family of Regular Maps of Type {6, 6}
%J Canadian mathematical bulletin
%D 1962
%P 13-20
%V 5
%N 1
%U http://geodesic.mathdoc.fr/articles/10.4153/CMB-1962-003-7/
%R 10.4153/CMB-1962-003-7
%F 10_4153_CMB_1962_003_7

[1] 1. Brahana, H. R., Regular Maps and their Groups, Amer. J. Math., 49 (1927), 268-84. Google Scholar

[2] 2. Coxeter, H. S. M., The Abstract Groups Gm, n, p , Trans. Amer. Math. Soc. 45 (1939), 73-150. Google Scholar

[3] 3. Coxeter, H. S. M., Regular Polytopes (London, 1948). Google Scholar

[4] 4. Coxeter, H. S. M., Configurations and Maps, Reports of a Math. Colloq. (2), 8 (1948), 18-38. Google Scholar

[5] 5. Coxeter, H. S. M., Introduction to Geometry (New York, 1961). Google Scholar

[6] 6. Coxeter, H. S. M. and Moser, W. O. J., Generators and Relations for Discrete Groups, Ergebn. Math., 14 (1957). Google Scholar

[7] 7. Frucht, R., A One-regular Graph of Degree Three, Can. J. Math., 4 (1952), 240-7. Google Scholar

[8] 8. Sherk, F. A., The Regular Maps on a Surface of Genus Three, Can. J. Math., 11 (1959), 452-480. Google Scholar

Cité par Sources :