Polyabolo
A polyabolo is an analog of the polyomino composed of 
isosceles
right triangles joined along edges of the same length. Polyaboloes are sometimes
also called polytans (Clark, Vichera).
Polyaboloes are considered equivalent if they have the same boundaries. For example, the two triaboloes illustrated above are considered equivalent. The number of nonequivalent
fixed polyaboloes composed of 
triangles are 1,
3, 4, 14, 30, 107, 318, 1116, 3671, ... (OEIS A006074).
Several of the know pairs of isospectral manifolds are polyaboloes.
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diabolo