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Constructions of chiral polytopes of small rank

By Antonio Breda d'Azevedo, Gareth Jones and Egon Schulte


An abstract polytope of rank n is said to be chiral if its automorphism group has precisely two orbits on the flags, such that adjacent flags belong to distinct orbits. The present paper describes a general method for deriving new finite chiral polytopes from old finite chiral polytopes of the same rank. In particular, the technique is used to construct many new examples in ranks 3, 4 and 5

Topics: QA
Year: 2011
OAI identifier:
Provided by: e-Prints Soton

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  1. A construction of higher rank chiral polytopes, doi
  2. (1960). A family of simple groups associated with the simple Lie algebra of type (G2), doi
  3. (1981). A symmetrical arrangement of eleven hemi-icosahedra. doi
  4. (2002). Abstract Regular Polytopes, in: doi
  5. (1999). All polytopes are quotients, and isomorphic polytopes are quotients by conjugate subgroups, doi
  6. (1985). Atlas of Finite Groups, doi
  7. (1991). Chiral Polytopes, doi
  8. (1994). Chirality and projective linear groups, doi
  9. (2009). Chirality groups of maps and hypermaps, doi
  10. (1987). Complex Functions, doi
  11. (2008). Constructions for chiral polytopes, doi
  12. (2000). Double coverings and reflexible hypermaps, doi
  13. (1997). Eisenstein integers and related C-groups,
  14. (1967). Endliche Gruppen I, doi
  15. (2007). Epimorphic images of simplicial Coxeter groups and some associated hyperbolic manifolds, PhD Thesis,
  16. Epimorphic images of the [5,3,5] Coxeter group, doi
  17. (2007). F-actions and parallel-product decomposition of reflexible maps, doi
  18. (1982). Finite Groups III, doi
  19. (1995). Free extensions of chiral polytopes, doi
  20. Generalized CPR-graphs and applications,
  21. (1980). Generators and Relations for Discrete Groups, 4th editon, doi
  22. (1967). Generators of the linear fractional groups, doi
  23. (1957). Geometric Algebra, Interscience, doi
  24. (2007). Groups of type L2(q) acting on polytopes, doi
  25. (1990). Hermitian forms and locally toroidal regular polytopes, doi
  26. (1990). Hurwitz groups: a brief survey, doi
  27. Hyperbolic manifolds and tessellations of type {3,5,3} associated with L2(q), in preparation.
  28. (2001). Join and intersection of hypermaps, doi
  29. (1958). Linear groups: With an exposition of the Galois field theory (with an introduction by W. Magnus), doi
  30. (1994). Maps, hypermaps and triangle groups, In The Grothendieck theory of dessins denfants, doi
  31. (2009). Modular reduction in abstract polytopes, doi
  32. Monodromy groups and self-invariance, doi
  33. (1962). On a class of doubly transitive groups, doi
  34. (2009). On locally spherical polytopes of type {5,3,5}, doi
  35. (1994). Parallel products in groups and maps, doi
  36. (2009). private communication,
  37. (2007). Reflection groups and polytopes over finite fields, doi
  38. (1990). Regular 4-polytopes related to general orthogonal groups, doi
  39. (2009). Regular maps and hypermaps of Euler characteristic −1 to −200, doi
  40. (1992). Regular polytopes of type {4,4,3} and {4,4,4}, doi
  41. (1977). Regularity of graphs, complexes and designs, In Probl` emes combinatoires et th´ eorie des graphes,
  42. (1980). Rotary maps of type {6,6}4, doi
  43. (2005). Self-duality of chiral polytopes, doi
  44. (2005). Sir´ aˇ n, Classification of regular maps of negative prime Euler characteristic,
  45. Sir´ aˇ n, The genera of chiral orientably-regular maps,
  46. (1993). Suzuki groups and surfaces, doi
  47. (1999). Symmetric tessellations on euclidean spaceforms, doi
  48. (1982). Ten toroids and fifty-seven hemi-dodecahedra, doi
  49. The chirality group and the chirality index of the Coxeter chiral maps, doi
  50. (1998). The groups of the regular star-polytopes. doi
  51. (1978). The smallest non-toroidal chiral maps, doi
  52. (1984). Twisted honeycombs {3,5,3}t and their groups, doi
  53. (1983). Twisted honeycombs {3,5,3}t,
  54. (1970). Twisted Honeycombs, Regional Conference Series in Mathematics,

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