Geodesic
Hypertopes with tetrahedral diagram
Domenico Catalano1 ; M. Elisa Fernandes1 ; Isabel Hubard2 ; Dimitri Leemans3
1Center for Research and Development in Mathematics and Applications, Department of Mathematics, University of Aveiro, Portugal
2Instituto de Matemáticas, Universidad Nacional Autónoma de México, Ciudad Universitaria, México D.F. 04510
3Département de Mathématique, C.P. 216 - Algébre et Combinatoire, Université Libre de Bruxelles, Boulevard du Triomphe, 1050 Brussels, Belgium
The electronic journal of combinatorics, Tome 25 (2018) no. 3
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In this paper we construct an infinite family of hypertopes of rank four having the complete graph $K_4$ as diagram. Their group of rotational symmetries is isomorphic to $PSL(2,q)$. It turns out some elements of this family are regular hypertopes and some are chiral. Moreover, we show that the chiral ones have both improper and proper correlations simultaneously.
DOI : 10.37236/7158
Classification : 52B11, 51E24, 20F05, 52B15
Mots-clés : regularity, chirality, thin geometries, hypermaps, abstract polytopes, chiral polytopes

Domenico Catalano  1   ; M. Elisa Fernandes  1   ; Isabel Hubard  2   ; Dimitri Leemans  3

1 Center for Research and Development in Mathematics and Applications, Department of Mathematics, University of Aveiro, Portugal
2 Instituto de Matemáticas, Universidad Nacional Autónoma de México, Ciudad Universitaria, México D.F. 04510
3 Département de Mathématique, C.P. 216 - Algébre et Combinatoire, Université Libre de Bruxelles, Boulevard du Triomphe, 1050 Brussels, Belgium 
@article{10_37236_7158,
     author = {Domenico Catalano and M. Elisa Fernandes and Isabel Hubard and Dimitri Leemans},
     title = {Hypertopes with tetrahedral diagram},
     journal = {The electronic journal of combinatorics},
     year = {2018},
     volume = {25},
     number = {3},
     doi = {10.37236/7158},
     zbl = {1402.52012},
     url = {http://geodesic.mathdoc.fr/articles/10.37236/7158/}
}
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Domenico Catalano; M. Elisa Fernandes; Isabel Hubard; Dimitri Leemans. Hypertopes with tetrahedral diagram. The electronic journal of combinatorics, Tome 25 (2018) no. 3. doi: 10.37236/7158

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