Proceedings of the Edinburgh Mathematical Society

Table of Contents - Volume 41 - 1922  

Research Article

Space-filling Tetrahedra in Euclidean Space

Professor D. M. Y. Sommerville

In the answer to the book-work question, set in a recent examination to investigate the volume of a pyramid, one candidate stated that the three tetrahedra into which a triangular prism can be divided are congruent, instead of only equal in volume. It was an interesting question to determine the conditions in order that the three tetrahedra should be congruent, and this led to the wider problem – to determine what tetrahedra can fill up space by repetitions. An exhaustive examination of this required one to keep an open mind as regards whether space is euclidean, elliptic, or hyperbolic, and then to pick out the forms which exist in euclidean space.

(Received April 06 1922)

(Accepted June 09 1922)