Editing Polyabolo (section)

==Tiling rectangles with copies of a single polyabolo==

[[Image:orderPolyabolos.png|Tiling rectangles with polyaboloes.|thumb|right]]

In 1968, [[David A. Klarner]] defined the ''order'' of a polyomino. Similarly, the order of a polyabolo P can be defined as the minimum number of congruent copies of P that can be assembled (allowing translation, rotation, and reflection) to form a [[rectangle]].

A polyabolo has order 1 if and only if it is itself a rectangle. Polyaboloes of order 2 are also easily recognisable. [[Solomon W. Golomb]] found polyaboloes, including a triabolo, of order 8.<ref>{{cite book
|last=Golomb |first=Solomon W.
|title=Polyominoes (2nd ed.)
|title-link= Polyominoes: Puzzles, Patterns, Problems, and Packings |publisher=Princeton University Press
|year=1994 |page=[https://archive.org/details/polyominoespuzzl00golo/page/n111 101] |isbn=0-691-02444-8}}</ref> Michael Reid found a heptabolo of order 6.<ref>{{cite book
|editor1-last=Goodman |editor1-first=Jacob E.|editor1-link=Jacob E. Goodman|editor2-last=O'Rourke|editor2-first= Joseph
|title=Handbook of Discrete and Computational Geometry (2nd ed.)
|publisher=Chapman & Hall/CRC
|year=2004 |page=349
|isbn=1-58488-301-4}}</ref>
Higher orders are possible.

There are interesting tessellations of the [[Euclidean plane]] involving polyaboloes.  One such is the [[tetrakis square tiling]], a [[Tessellation#Monohedral|monohedral tessellation]] that fills the entire Euclidean plane with 45–45–90 triangles.
[[Image:order20Polyabolo.png|A polyabolo of order 20.|thumb|right]]