Geodesic
Many neighborly inscribed polytopes and Delaunay triangulations
Discrete mathematics & theoretical computer science, DMTCS Proceedings vol. AT, 26th International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2014), DMTCS Proceedings vol. AT, 26th International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2014) (2014).

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We present a very simple explicit technique to generate a large family of point configurations with neighborly Delaunay triangulations. This proves that there are superexponentially many combinatorially distinct neighborly $d$-polytopes with $n$ vertices that admit realizations inscribed on the sphere. These are the first examples of inscribable neighborly polytopes that are not cyclic polytopes, and provide the current best lower bound for the number of combinatorial types of inscribable polytopes (and thus also of Delaunay triangulations). It coincides with the current best lower bound for the number of combinatorial types of polytopes. 
@article{DMTCS_2014_special_265_a14,
     author = {Gonska, Bernd and Padrol, Arnau},
     title = {Many neighborly inscribed polytopes and {Delaunay} triangulations},
     journal = {Discrete mathematics & theoretical computer science},
     publisher = {mathdoc},
     volume = {DMTCS Proceedings vol. AT, 26th International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2014)},
     year = {2014},
     doi = {10.46298/dmtcs.2389},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.46298/dmtcs.2389/}
}
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%D 2014
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Gonska, Bernd; Padrol, Arnau. Many neighborly inscribed polytopes and Delaunay triangulations. Discrete mathematics & theoretical computer science, DMTCS Proceedings vol. AT, 26th International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2014), DMTCS Proceedings vol. AT, 26th International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2014) (2014). doi : 10.46298/dmtcs.2389. http://geodesic.mathdoc.fr/articles/10.46298/dmtcs.2389/

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