Integrable lattices of hyperplanes related to billiards within confocal quadrics

Milena Radnović
2015 Publications de l'Institut Math?matique (Belgrade)   unpublished
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.