An enumeration of equilateral triangle dissections

Authors:
Aleš Drápal;Carlo Hämäläinen
Affiliations:
Department of Mathematics, Charles University, Sokolovská 83, 186 75 Praha 8, Czech Republic;Department of Mathematics, Charles University, Sokolovská 83, 186 75 Praha 8, Czech Republic
Venue:
Discrete Applied Mathematics
Year:
2010

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Abstract

We enumerate all dissections of an equilateral triangle into smaller equilateral triangles up to size 20, where each triangle has integer side lengths. A perfect dissection has no two triangles of the same side, counting up- and down-oriented triangles as different. We computationally prove Tutte's conjecture that the smallest perfect dissection has size 15 and we find all perfect dissections up to size 20.