Exactly solvable quantum few-body systems associated with the symmetries   of the three-dimensional and four-dimensional icosahedra
  The purpose of this article is to demonstrate that non-crystallographic reflection groups can be used to build new solvable quantum particle systems. We explicitly construct a one-parametric family of solvable four-body systems on a line, related to the symmetry of a regular icosahedron: in two distinct limiting cases the system is constrained to a half-line. We repeat the program for a 600-cell, a four-dimensional generalization of the regular three-dimensional icosahedron. 
T. Scoquart, J. J. Seaward, S. G. Jackson, M. Olshanii
math-ph cond-mat.quant-gas math.MP nlin.SI