A polyabolo is an analog of the polyomino composed of congruent isosceles right triangles joined along entire
edges of the same length, with nonoverlapping interiors ,
where positive
integer . Polyaboloes are sometimes also called polytans (Clarke, Vicher).
Polyaboloes are considered equivalent if they have the same boundaries . For example, the two triaboloes illustrated above are considered equivalent. Translations ,
rotations , and reflections
are counted as equivalent. The numbers of free polyaboloes composed of triangles are 1, 3, 4, 14, 30,
107, 318, 1116, 3743, ... (OEIS A006074 ).
Several of the known pairs of isospectral manifolds
are polyaboloes.
See also Diabolo ,
Hexabolo ,
Isosceles Right Triangle ,
Isospectral
Manifolds ,
Pentabolo ,
Polyform ,
Polyiamond ,
Tetrabolo ,
Triabolo
Explore with Wolfram|Alpha
References Clarke, A. L. "Polyaboloes." https://web.archive.org/web/20060616100026/http://www.recmath.com/PolyPages/PolyPages/Polyaboloes.htm . Keller, M. "Counting Polyforms." https://www.solitairelaboratory.com/polyenum.html . Sloane,
N. J. A. Sequence A006074 /M2379
in "The On-Line Encyclopedia of Integer Sequences." Vicher,
M. "Polyforms." https://web.archive.org/web/20250831090700/https://www.vicher.cz/puzzle/polyforms.htm . Referenced
on Wolfram|Alpha Polyabolo
Cite this as:
Weisstein, Eric W. "Polyabolo." From MathWorld https://mathworld.wolfram.com/Polyabolo.html
Subject classifications
congruent isosceles right triangles joined along entire
edges of the same length, with nonoverlapping interiors,
where 
is a positive
integer. Polyaboloes are sometimes also called polytans (Clarke, Vicher).
triangles are 1, 3, 4, 14, 30,
107, 318, 1116, 3743, ... (OEIS A006074).
