, Volume 37, Issue 2, pp 287-296

Sommerville's Missing Tetrahedra

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Abstract

D.M.Y. Sommerville's 1923 classification of tetrahedra that can tile 3-space in a proper, face-to-face manner is completed, by showing that the case he failed to consider cannot occur, although it does occur in non-proper and in non-face-to-face tilings.