# Rectangles Tiled with Three Didrafters

## Introduction

A didrafter is a polyform made by joining two drafters, 30°-60°-90° right triangles, at their short legs, long legs, hypotenuses, or half hypotenuses. Polydrafters joined on the polyiamond (triangle) grid are called proper polydrafters. Polydrafters whose cells depart from the grid are called extended polydrafters. Here are the 13 didrafters, proper and extended:

Below I show how to make a minimal rectangle using copies of three didrafters, at least one of each. These solutions are not necessarily unique, nor are their tilings. If you find a solution with fewer tiles, or solve an unsolved case, please write.

 1-2-3 6 1-4-10 × 1-8-10 × 2-4-7 × 2-7-12 × 3-5-6 × 3-9-10 × 4-7-9 × 5-6-13 8 6-7-12 × 7-10-11 × 1-2-4 10 1-4-11 × 1-8-11 × 2-4-8 × 2-7-13 × 3-5-7 × 3-9-11 × 4-7-10 × 5-7-8 × 6-7-13 16 7-10-12 × 1-2-5 8 1-4-12 × 1-8-12 × 2-4-9 6 2-8-9 16 3-5-8 × 3-9-12 × 4-7-11 × 5-7-9 × 6-8-9 × 7-10-13 × 1-2-6 10 1-4-13 × 1-8-13 × 2-4-10 × 2-8-10 × 3-5-9 × 3-9-13 × 4-7-12 × 5-7-10 × 6-8-10 3 7-11-12 × 1-2-7 40 1-5-6 21 1-9-10 × 2-4-11 × 2-8-11 × 3-5-10 × 3-10-11 × 4-7-13 × 5-7-11 × 6-8-11 14 7-11-13 × 1-2-8 12 1-5-7 × 1-9-11 × 2-4-12 × 2-8-12 × 3-5-11 × 3-10-12 × 4-8-9 × 5-7-12 × 6-8-12 × 7-12-13 × 1-2-9 6 1-5-8 6 1-9-12 × 2-4-13 × 2-8-13 × 3-5-12 × 3-10-13 × 4-8-10 × 5-7-13 × 6-8-13 8 8-9-10 × 1-2-10 10 1-5-9 × 1-9-13 × 2-5-6 3 2-9-10 8 3-5-13 × 3-11-12 × 4-8-11 × 5-8-9 × 6-9-10 4 8-9-11 × 1-2-11 18 1-5-10 × 1-10-11 × 2-5-7 × 2-9-11 16 3-6-7 × 3-11-13 × 4-8-12 × 5-8-10 × 6-9-11 8 8-9-12 × 1-2-12 × 1-5-11 × 1-10-12 × 2-5-8 × 2-9-12 × 3-6-8 × 3-12-13 × 4-8-13 × 5-8-11 × 6-9-12 × 8-9-13 × 1-2-13 70 1-5-12 × 1-10-13 × 2-5-9 10 2-9-13 16 3-6-9 8 4-5-6 4 4-9-10 × 5-8-12 × 6-9-13 14 8-10-11 × 1-3-4 6 1-5-13 × 1-11-12 × 2-5-10 × 2-10-11 × 3-6-10 × 4-5-7 × 4-9-11 × 5-8-13 × 6-10-11 × 8-10-12 × 1-3-5 16 1-6-7 12 1-11-13 × 2-5-11 × 2-10-12 × 3-6-11 × 4-5-8 × 4-9-12 × 5-9-10 × 6-10-12 × 8-10-13 × 1-3-6 12 1-6-8 60 1-12-13 × 2-5-12 × 2-10-13 × 3-6-12 × 4-5-9 × 4-9-13 × 5-9-11 × 6-10-13 × 8-11-12 × 1-3-7 6 1-6-9 8 2-3-4 × 2-5-13 × 2-11-12 × 3-6-13 × 4-5-10 × 4-10-11 × 5-9-12 × 6-11-12 × 8-11-13 × 1-3-8 16 1-6-10 × 2-3-5 × 2-6-7 × 2-11-13 × 3-7-8 × 4-5-11 × 4-10-12 × 5-9-13 × 6-11-13 × 8-12-13 × 1-3-9 × 1-6-11 × 2-3-6 × 2-6-8 × 2-12-13 × 3-7-9 × 4-5-12 × 4-10-13 × 5-10-11 × 6-12-13 × 9-10-11 × 1-3-10 6 1-6-12 × 2-3-7 × 2-6-9 6 3-4-5 × 3-7-10 × 4-5-13 × 4-11-12 × 5-10-12 × 7-8-9 × 9-10-12 × 1-3-11 × 1-6-13 × 2-3-8 × 2-6-10 × 3-4-6 × 3-7-11 × 4-6-7 × 4-11-13 × 5-10-13 × 7-8-10 × 9-10-13 × 1-3-12 × 1-7-8 × 2-3-9 16 2-6-11 8 3-4-7 × 3-7-12 × 4-6-8 8 4-12-13 × 5-11-12 × 7-8-11 × 9-11-12 × 1-3-13 × 1-7-9 × 2-3-10 × 2-6-12 × 3-4-8 × 3-7-13 × 4-6-9 8 5-6-7 × 5-11-13 × 7-8-12 × 9-11-13 × 1-4-5 × 1-7-10 × 2-3-11 × 2-6-13 × 3-4-9 × 3-8-9 × 4-6-10 × 5-6-8 × 5-12-13 × 7-8-13 × 9-12-13 × 1-4-6 12 1-7-11 × 2-3-12 × 2-7-8 × 3-4-10 × 3-8-10 × 4-6-11 × 5-6-9 × 6-7-8 × 7-9-10 × 10-11-12 × 1-4-7 × 1-7-12 × 2-3-13 × 2-7-9 × 3-4-11 × 3-8-11 × 4-6-12 × 5-6-10 12 6-7-9 × 7-9-11 × 10-11-13 × 1-4-8 × 1-7-13 × 2-4-5 × 2-7-10 × 3-4-12 × 3-8-12 × 4-6-13 × 5-6-11 24 6-7-10 × 7-9-12 × 10-12-13 × 1-4-9 × 1-8-9 × 2-4-6 3 2-7-11 × 3-4-13 × 3-8-13 × 4-7-8 × 5-6-12 × 6-7-11 12 7-9-13 × 11-12-13 ×

## 70 Tiles

Last revised 2020-06-29.

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Col. George Sicherman [ HOME | MAIL ]