Galaxies from the 14 Tridrafters

A tridrafter is a polyform made by joining three equal 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. There are 14 proper tridrafters.

How can the 14 proper tridrafters be arranged to form a galaxy, a shape with sixfold rotary symmetry?

These shapes were first tiled by Bob Harris, who called them the pinwheel and the sawblade. The shape on the left has 10 tilings. The shape on the right has 2. Patrick Hamlyn has determined that only these two 6-rotary shapes can be formed by the 14 tridrafters. Todor Tchervenkov has confirmed my tiling counts.

Last revised 2021-04-11.

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Col. George Sicherman [ HOME | MAIL ]