Trivalent Polygonal Complexes of Nonpositive Curvature and Platonic Symmetry

Geometriae Dedicata

Volumn 70, Issue 1, 1998, Pages 87-110

  Świa̧tkowski, Jacek ^a  

^a UNIVERSITY OF WROC AW   (Poland)

Author keywords

Automorphism group; Nonpositive curvature; Polyhedral complex

Indexed keywords

EID: 0042728281     PISSN: 00465755     EISSN: None     Source Type: Journal    
DOI: 10.1023/A:1004954009167     Document Type: Article

References (15)

1. Ballmann, W. and Brin, M.: Polygonal complexes and combinatorial group theory, Geom. Dedicata 50 (1994), 165-191.
2. Benakli, N.: Polyèdre à géométrie locale donnée, C.R. Acad. Sci. Paris 313, Serie I (1991), 561-564.
3. Benakli, N.: Polyèdre hyperbolique à groupe d'automorphismes non discret, C.R. Acad. Sci. Paris 313, Serie I (1991), 667-669.
4. Biggs, N. L.: Constructing 5-arc-transitive cubic graphs, J. London Math. Soc. 26 (1982), 193-200.
5. Bouwer, I. Z. (ed.): The Foster Census, Winnipeg, 1988.
6. Conder, M. and Lorimer, P.: Automorphism groups of symmetric graphs of valency 3, J. Combin. Theory B47 (1989), 60-72.
7. Coxeter, H. S. M.: Self-dual configurations and regular graphs, Bull. Amer. Math. Soc. 56 (1950), 413-455.
8. Djokovič, D. and Miller, G.: Regular groups of automorphisms of cubic graphs, J. Combin. Theory B29 (1980), 195-230.
9. Frucht, R.: A one-regular graph of degree 3, Canad. J. Math. 4 (1952), 240-247.
10. Gromov, M.: Hyperbolic groups, in S. Gersten (ed.), Essays in Group Theory, Springer Verlag, New York, 1987, pp. 75-263.
11. Haefliger, A.: Complexes of groups and orbihedra, in E. Ghys, A. Haefliger and A. Verjovsky (eds), Group Theory from a Geometrical Viewpoint (Trieste, 1990), World Scientific, 1991, pp. 504-540.
12. Haglund, F.: Les polyèdres de Gromov, C.R. Acad. Sci. Paris 313, Serie I (1991), 603-606.
13. Ronan, M.: Lectures on Buildings, Academic Press, Boston, 1989.
14. Tits, J.: Spheres of radius 2 in triangle buildings, in W. Kantor, R. Liebler, S. Payne and E. Shult (eds), Finite Geometries, Building and Related Topics (Pingree Park, 1988), Clarendon Press, Oxford, 1990, pp. 17-28.
15. Tutte, W. T.: A family of cubical graphs, Proc. Cambridge Philos. Soc. 43 (1947), 459-474.