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.

See also Convex Figures with Didrafter Triplets.

1-2-36 1-4-10× 1-8-10× 2-4-7× 2-7-12× 3-5-6× 3-9-10× 4-7-9× 5-6-138 6-7-12× 7-10-11×
1-2-410 1-4-11× 1-8-11× 2-4-8× 2-7-13× 3-5-7× 3-9-11× 4-7-10× 5-7-8× 6-7-1316 7-10-12×
1-2-58 1-4-12× 1-8-12× 2-4-96 2-8-916 3-5-8× 3-9-12× 4-7-11× 5-7-9× 6-8-9× 7-10-13×
1-2-610 1-4-13× 1-8-13× 2-4-10× 2-8-10× 3-5-9× 3-9-13× 4-7-12× 5-7-10× 6-8-103 7-11-12×
1-2-740 1-5-621 1-9-10× 2-4-11× 2-8-11× 3-5-10× 3-10-11× 4-7-13× 5-7-11× 6-8-1114 7-11-13×
1-2-812 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×
1-2-96 1-5-86 1-9-12× 2-4-13× 2-8-13× 3-5-12× 3-10-13× 4-8-10× 5-7-13× 6-8-138 8-9-10×
1-2-1010 1-5-9× 1-9-13× 2-5-63 2-9-108 3-5-13× 3-11-12× 4-8-11× 5-8-9× 6-9-104 8-9-11×
1-2-1118 1-5-10× 1-10-11× 2-5-7× 2-9-1116 3-6-7× 3-11-13× 4-8-12× 5-8-10× 6-9-118 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×
1-2-1370 1-5-12× 1-10-13× 2-5-910 2-9-1316 3-6-98 4-5-64 4-9-10× 5-8-12× 6-9-1314 8-10-11×
1-3-46 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×
1-3-516 1-6-712 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×
1-3-612 1-6-860 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×
1-3-76 1-6-98 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×
1-3-816 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×
1-3-106 1-6-12× 2-3-7× 2-6-96 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× 2-3-916 2-6-118 3-4-7× 3-7-12× 4-6-88 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× 4-6-98 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×
1-4-612 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× 5-6-1012 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× 5-6-1124 6-7-10× 7-9-12× 10-12-13×
1-4-9× 1-8-9× 2-4-63 2-7-11× 3-4-13× 3-8-13× 4-7-8× 5-6-12× 6-7-1112 7-9-13× 11-12-13×

3 Tiles

4 Tiles

6 Tiles

8 Tiles

10 Tiles

12 Tiles

14 Tiles

16 Tiles

18 Tiles

21 Tiles

24 Tiles

40 Tiles

60 Tiles

70 Tiles

Last revised 2020-06-29.


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Col. George Sicherman [ HOME | MAIL ]