An enumeration of equilateral triangle dissections

TL;DR

This paper computationally enumerates all possible dissections of an equilateral triangle into smaller equilateral triangles with integer sides up to size 20, confirming Tutte's conjecture about the smallest perfect dissection size.

Contribution

It provides a complete enumeration of equilateral triangle dissections up to size 20 and proves Tutte's conjecture that the smallest perfect dissection has size 15.

Findings

Confirmed Tutte's conjecture about the smallest perfect dissection size.

Enumerated all dissections up to size 20.

Identified all perfect dissections within the size range.

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 W. T. Tutte's conjecture that the smallest perfect dissection has size 15 and we find all perfect dissections up to size 20.