Chiral polytope

Chiral polytope
A snub cube comes in two mirror image chiral copies, shown here as alternations of a great rhombicuboctahedron

In mathematics, a polytope P is chiral if it has two orbits of flags under its group of symmetries, with adjacent flags in different orbits.

See also

References

  • Schulte, E. Chiral polytopes in ordinary space, I. Discrete Comput. Geom. 32 (2004), 55–99.
  • Schulte, E. and Weiss, A.I. Chiral polytopes. In Applied Geometry and Discrete Mathematics (The Victor Klee Festschrift), DIMACS Series in Discrete Mathematics and Theoretical Computer Science, vol. 4, eds. Gritzmann, P. and Sturmfels, B., Amer. Math. Soc. and Assoc. Computing Machinery, 1991, 493–516.
  • Monson, B., Pisanski, T., Schulte, E., and Ivić Weiss, A. 2007. Semisymmetric graphs from polytopes. J. Comb. Theory Ser. A 114, 3 (Apr. 2007), 421-435. DOI=http://dx.doi.org/10.1016/j.jcta.2006.06.007
  • Hubard, I. and Weiss, A. I. 2005. Self-duality of chiral polytopes. J. Comb. Theory Ser. A 111, 1 (Jul. 2005), 128-136. DOI= http://dx.doi.org/10.1016/j.jcta.2004.11.012
  • Conder, M., Hubard, I., and Pisanski, T. Constructions for chiral polytopes, J. London Math. Soc. 77 (2008) 115-129.
  • Monson, B., Ivić Weiss, A., Cayley Graphs and Symmetric 4-Polytopes, Ars Mathematica Contemporanea 1 (2008) 185–205.

External links

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