References
Bourbaki, N.: Groupes et algèbres de Lie, Ch. 4–6. Actu. Sci. Ind. Paris: Hermann 1968
Buekenhout, F.: Diagrams for geometries and groups J. Comb. Theory A27, 121–151 (1979)
Carter, R.W.: Simple groups of Lie type, Pure and Applied Mathematics Vol. 28, London: Wiley & Sons 1972
Colbourn, C.J., Weiss, A.I.: A census of regular 3-polystroma arising from honeycombs. Discrete Math.50, 29–36 (1984)
Coxeter, H.S.M.: The abstract groupsR m=S m=(R j S j)pj=1,S m=T 2=(S j T)2pj=1, andS m=T 2=S −j TS j T)pj=1., Proc. London Math. Soc. (2),41, 278–301 (1936)
Coxeter, H.S.M.: Regular skew polyhedra in 3 and 4 dimensions and their topological analogues. Proc. Lond. Math. Soc. (2),43, 33–62 (1937), (reprinted with amendments in ‘Twelve geometric essays’, Southern Illinois University Press Carbondale, 1968)
Coxeter, H.S.M.: Groups generated by unitary reflections of period two. Can. J. Math.9, 243–272 (1957)
Coxeter, H.S.M.: Regular polytopes, 3rd edition. New York: Dover 1973
Coxeter, H.S.M.: Regular complex polytopes. Cambridge: Cambridge University Press 1974
Coxeter, H.S.M., Moser, W.O.J.: Generators and relations for discrete groups 4th edition. Berlin Heidelberg New York: Springer 1980
Coxeter, H.S.M., Shephard, G.C.: Regular 3-complexes with toroidal cells. J. Comb. Theory B22, 131–138 (1977)
Danzer, L.: Regular incidence-complexes and dimensionally unbounded sequences of such (I). Ann. Discrete Math.20, 115–127 (1984), (part II in preparation)
Danzer, L., Schulte, E.: Reguläre Inzidenzkomplexe I. Geometriae dedicata13, 295–308 (1982)
Dress, A.W.M.: A combinatorial theory of Grünbaum's new regular polyhedra, Part I: Grünbaum's new regular polyhedra and their automorphism group Aequationes Math.23, 252–265 (1981)
Dress, A.W.M.: Regular polytopes and equivariant tessellations from a combinatorial point of view. Proc. Conf. Algebraic Topology, Göttingen, 1984, SLN
Grünbaum, B.: Regular polyhedra — old and new. Aequationes Math.16, 1–20 (1977)
Grünbaum, B.: Regularity of graphs, complexes and designs, in ‘Problèmes, combinatoire et théorie des graphes’. Coll. Int. CNRS No. 260, Orsay, 1977, 191–197
McMullen, P.: Combinatorially regular polytopes. Mathematika14, 142–150 (1967)
McMullen, P.: Regular star-polytopes and a theorem of Hess Proc. Lond. Math. Soc. (3)18, 577–596 (1968)
McMullen, P.: Realizations of regular polytopes. Aequationes Math., in press
McMullen, P., Schulte, E.: Regular polytopes from twisted Coxeter groups and unitary reflexion groups. Advances in Mathematics, in press
McMullen, P., Schulte, E., Wills, J.M.: Infinite series of combinatorially regular polyhedra in three-space. Geometriae dedicata26, 299–307 (1988)
Schulte, E.: Reguläre Inzidenzkomplexe II. Geometriae dedicata14, 33–56 (1983)
Schulte, E.: Extensions of regular complexes, in: Lectures notes in pure and applied mathematics 103, Finite Geometries, 289–305 (edit. by C.A. Baker and L.M. Batten). New York: Marcel Dekker 1985
Schulte, E.: Amalgamations of regular incidence-polytopes. Proc. Lond. Math. Soc. (3)56, 303–328 (1988)
Shephard, G.C.: Regular complex polytopes. Proc. Lond. Math. Soc. (3)2, 82–97 (1952)
Shephard, G.C., Todd, J.A.: Finite unitary reflection groups. Can. J. Math.6, 274–304 (1954)
Tits, J.: Groupes et géométries de Coxeter, notes polycopiées, IHES, Paris, 1961
Tits, J.: A local approach to buildings, in ‘The geometric vein (The Coxeter-Festschrift)’, edit. by Ch. Davis, B. Grünbaum and F.A. Sherk, 519–547. Berlin Heidelberg New York: Springer 1981
Weiss, A.I.: Incidence-polytopes of type {6, 3, 3,}. Geometriae dedicata20, 147–155 (1986)
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Dedicated to Professor L. Danzer on the occasion of his 60th birthday
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McMullen, P., Schulte, E. Regular polytopes from twisted Coxeter groups. Math Z 201, 209–226 (1989). https://doi.org/10.1007/BF01160678
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DOI: https://doi.org/10.1007/BF01160678