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Polydrafter

Geometric shape formed of right triangles

Summary

Geometric shape formed of right triangles

In recreational mathematics, a polydrafter is a polyform with a 30°–60°–90° right triangle as the base form. This triangle is also called a drafting triangle, hence the name.{{citation | editor1-last = Dai | editor1-first = Jian S. | editor2-last = Zoppi | editor2-first = Matteo | editor3-last = Kong | editor3-first = Xianwen

History

Polydrafters were invented by Christopher Monckton, who used the name polydudes for polydrafters that have no cells attached only by the length of a short leg. Monckton's Eternity Puzzle was composed of 209 12-dudes.

The term polydrafter was coined by Ed Pegg Jr., who also proposed as a puzzle the task of fitting the 14 tridrafters—all possible clusters of three drafters—into a trapezoid whose sides are 2, 3, 5, and 3 times the length of the hypotenuse of a drafter.

Extended polydrafters

An extended polydrafter is a variant in which the drafter cells cannot all conform to the triangle (polyiamond) grid. The cells are still joined at short legs, long legs, hypotenuses and half-hypotenuses. See the Logelium link below.

Enumerating polydrafters

Like polyominoes, polydrafters can be enumerated in two ways, depending on whether chiral pairs of polydrafters are counted as one polydrafter or two.

n	Name of
n-polydrafter	Number of n-polydrafters
(reflections counted separately)	Number
of free
n-polydudes	free
one-sided

1	monodrafter	1	2	1
2	didrafter	6	8	3
3	tridrafter	14	28	1
4	tetradrafter	64	116	9
5	pentadrafter	237	474	15
6	hexadrafter	1024	2001	59

With two or more cells, the numbers are greater if extended polydrafters are included. For example, the number of didrafters rises from 6 to 13. See .

References

Pickover, Clifford A.. (2009). "The Math Book: From Pythagoras to the 57th Dimension, 250 Milestones in the History of Mathematics". Sterling Publishing Company, Inc..
Pegg, Ed Jr.. (2005). "Tribute to a Mathemagician". A K Peters.

Wikipedia Source

This article was imported from Wikipedia and is available under the Creative Commons Attribution-ShareAlike 4.0 License. Content has been adapted to SurfDoc format. Original contributors can be found on the article history page.

polyforms

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