Mathematical and physical billiard in pyramids

Abstract

In this experimental work we study billiard trajectories in triangular pyramids and try to establish conditions that guarantee the existence (or absence) of 4-cycles (there can be not more, than three of them). We formulate conjectures and prove some statements. For example, if a pyramid has two orthogonal faces, then it has not more than two 4-cycles. Also we study 4-cycles of the "physical" billiard in pyramids, i.e. in the presence of gravity. Here we present our observations for a generic case.