Geodesic
Integrable Lattices of Hyperplanes Related to Billiards Within Confocal Quadrics
Publications de l'Institut Mathématique, _N_S_98 (2015) no. 112, p. 25 .

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We introduce a new discrete system that arises from ellipsoidal billiards and is closely related to the double reflection nets. The system is defined on the lattice of a uniform honeycomb consisting of rectified hypercubes and cross polytopes. In the 2-dimensional case, the lattice is regular and it incorporates dynamics both in the original space and its dual. In the 3-dimensional case, the lattice consists of tetrahedra and cuboctahedra.
DOI : 10.2298/PIM1512025R
Classification : 37J35;14H70;37D05;51N25
Keywords: billiard, confocal quadrics, discrete integrable systems, double reflection nets 
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     title = {Integrable {Lattices} of {Hyperplanes} {Related} to {Billiards} {Within} {Confocal} {Quadrics}},
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Milena Radnović. Integrable Lattices of Hyperplanes Related to Billiards Within Confocal Quadrics. Publications de l'Institut Mathématique, _N_S_98 (2015) no. 112, p. 25 . doi : 10.2298/PIM1512025R. http://geodesic.mathdoc.fr/articles/10.2298/PIM1512025R/

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