VI.—Division of Space by Congruent Triangles and Tetrahedra

Abstract

It is proposed to investigate the various ways in which it is possible to divide the plane into congruent triangles, and space of three dimensions into congruent tetrahedra. The method of inquiry will not at first reveal any distinction between elliptic, euclidean, and hyperbolic space; networks in all three spaces will be obtained concurrently, and they must be tested afterwards to determine the type of space to which they belong. In the first part we shall deal with the plane, and in the second part with space of three dimensions.