Sommerville's Missing Tetrahedra

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.

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1. Department of Mathematics, Indiana University, Bloomington, IN 47405, USA

   Allan L. Edmonds

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1. Allan L. Edmonds
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Correspondence to Allan L. Edmonds.

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Edmonds, A. Sommerville's Missing Tetrahedra. Discrete Comput Geom 37, 287–296 (2007). https://doi.org/10.1007/s00454-006-1293-4

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• Issue Date: February 2007

• DOI: https://doi.org/10.1007/s00454-006-1293-4

Keywords

• Dihedral Angle
• Edge Length
• Discrete Comput Geom
• Isosceles Triangle
• Triangular Prism