Geodesic
Mixing chiral polytopes
Journal of Algebraic Combinatorics, Tome 36 (2012) no. 2, pp. 263-277.

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Summary: An abstract polytope of rank n is said to be chiral if its automorphism group has two orbits on the flags, such that adjacent flags belong to distinct orbits. Examples of chiral polytopes have been difficult to find. A "mixing" construction lets us combine polytopes to build new regular and chiral polytopes. By using the chirality group of a polytope, we are able to give simple criteria for when the mix of two polytopes is chiral.
Keywords: abstract regular polytope, chiral polytope, chiral maps, chirality group 
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     author = {Cunningham, Gabe},
     title = {Mixing chiral polytopes},
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     url = {http://geodesic.mathdoc.fr/item/JAC_2012__36_2_a2/}
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Cunningham, Gabe. Mixing chiral polytopes. Journal of Algebraic Combinatorics, Tome 36 (2012) no. 2, pp. 263-277. http://geodesic.mathdoc.fr/item/JAC_2012__36_2_a2/