Classification of the Finite Compounds of Cubes

Abstract

A compound of cubes has been defined as the orbit of a centered cube for an action group G of isometries. As such, it is the expression of an isomorphic right G-set G/H, where H is the stabilizer of the descriptive position of the cube. In this part, such orbits will be constructed and classified for the finite groups of isometries, and discussed afterward. As has been explained, however, these groups may be restricted to those, containing I, which will be further referred to as I-groups (and I-subgroups).