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An ''extended polydrafter'' is a variant in which the drafter cells cannot all conform to the triangle (
The Eternity Puzzle
a
mathpuzzle.com
a
Logelium
{{Polyforms Polyforms
In recreational mathematics
Recreational mathematics is mathematics carried out for recreation (entertainment) rather than as a strictly research and application-based professional activity or as a part of a student's formal education. Although it is not necessarily limited ...
, a polydrafter is a polyform
In recreational mathematics, a polyform is a plane figure or solid compound constructed by joining together identical basic polygons. The basic polygon is often (but not necessarily) a convex plane-filling polygon, such as a square or a triangle ...
with a 30°–60°–90° right triangle
A right triangle (American English) or right-angled triangle ( British), or more formally an orthogonal triangle, formerly called a rectangled triangle ( grc, ὀρθόσγωνία, lit=upright angle), is a triangle in which one angle is a right ...
as the base form. This triangle is also called a drafting triangle, hence the name. This triangle is also half of an equilateral triangle
In geometry, an equilateral triangle is a triangle in which all three sides have the same length. In the familiar Euclidean geometry, an equilateral triangle is also equiangular; that is, all three internal angles are also congruent to each oth ...
, and a polydrafter's cells must consist of halves of triangles in the triangular tiling
In geometry, the triangular tiling or triangular tessellation is one of the three regular tilings of the Euclidean plane, and is the only such tiling where the constituent shapes are not parallelogons. Because the internal angle of the equilater ...
of the plane; consequently, when two drafters share an edge that is the middle of their three edge lengths, they must be reflections rather than rotations of each other. Any contiguous subset of halves of triangles in this tiling is allowed, so unlike most polyforms, a polydrafter may have cells joined along unequal edges: a hypotenuse and a short leg.
History
Polydrafters were invented byChristopher Monckton
Christopher Walter Monckton, 3rd Viscount Monckton of Brenchley (born 14 February 1952) is a British public speaker and hereditary peer. He is known for his work as a journalist, Conservative political advisor, UKIP political candidate, and fo ...
, who used the name ''polydudes'' for polydrafters that have no cells attached only by the length of a short leg. Monckton's Eternity Puzzle
The Eternity puzzle is a tiling puzzle created by Christopher Monckton and launched by the Ertl Company in June 1999. It was marketed as being practically unsolvable, with a £1 million prize on offer for whoever could solve it within four years. ...
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
A polyiamond (also polyamond or simply iamond, or sometimes triangular polyomino) is a polyform whose base form is an equilateral triangle. The word ''polyiamond'' is a back-formation from ''diamond'', because this word is often used to describe ...
) grid.
The cells are still joined at short legs, long legs, hypotenuses and half-hypotenuses.
See the Logelium link below.
Enumerating polydrafters
Likepolyomino
A polyomino is a plane geometric figure formed by joining one or more equal squares edge to edge. It is a polyform whose cells are squares. It may be regarded as a finite subset of the regular square tiling.
Polyominoes have been used in po ...
es, polydrafters can be enumerated in two ways, depending on whether chiral
Chirality is a property of asymmetry important in several branches of science. The word ''chirality'' is derived from the Greek (''kheir''), "hand", a familiar chiral object.
An object or a system is ''chiral'' if it is distinguishable from i ...
pairs of polydrafters are counted as one polydrafter or two.
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 .
See also
*Thekisrhombille tiling
In geometry, the truncated trihexagonal tiling is one of eight semiregular tilings of the Euclidean plane. There are one square, one hexagon, and one dodecagon on each vertex. It has Schläfli symbol of ''tr''.
Names
Uniform colorings
Th ...
, a tessellation of the plane made of 30°–60°–90° triangles.
References
External links
*The Eternity Puzzle
a
mathpuzzle.com
a
Logelium
{{Polyforms Polyforms