Polydrafter
Geometric shape formed of right triangles
title: "Polydrafter" type: doc version: 1 created: 2026-02-28 author: "Wikipedia contributors" status: active scope: public tags: ["polyforms"] description: "Geometric shape formed of right triangles" topic_path: "general/polyforms" source: "https://en.wikipedia.org/wiki/Polydrafter" license: "CC BY-SA 4.0" wikipedia_page_id: 0 wikipedia_revision_id: 0
::summary Geometric shape formed of right triangles ::
::figure[src="https://upload.wikimedia.org/wikipedia/commons/6/60/Monodrafter.png" caption="30–60–90 triangle"] ::
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 | last1 = Salvi | first1 = Anelize Zomkowski | last2 = Simoni | first2 = Roberto | last3 = Martins | first3 = Daniel | editor1-last = Dai | editor1-first = Jian S. | editor2-last = Zoppi | editor2-first = Matteo | editor3-last = Kong | editor3-first = Xianwen | contribution = Enumeration problems: A bridge between planar metamorphic robots in engineering and polyforms in mathematics | doi = 10.1007/978-1-4471-4141-9_3 | pages = 25–34 | publisher = Springer | title = Advances in Reconfigurable Mechanisms and Robots I | year = 2012| isbn = 978-1-4471-4140-2
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
::figure[src="https://upload.wikimedia.org/wikipedia/commons/6/6a/Extended_didrafters.png" caption="Two extended didrafters"] ::
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.
::data[format=table]
| 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
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.
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