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In recreational mathematics, a polyabolo (also known as a polytan) is a polyform with an isosceles right triangle as the base form. The name is a back formation from 'diabolo' although the shape formed by joining two triangles at just one vertex is not a proper polyabolo. On a false analogy as if di- in diabolo means twice, polyaboloes with from 1 to 10 triangles are called respectively monoboloes, diaboloes, triaboloes, tetraboloes, pentaboloes, hexaboloes, heptaboloes, octaboloes, enneaboloes, and decaboloes.

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  • Polyabolo
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  • In recreational mathematics, a polyabolo (also known as a polytan) is a polyform with an isosceles right triangle as the base form. The name is a back formation from 'diabolo' although the shape formed by joining two triangles at just one vertex is not a proper polyabolo. On a false analogy as if di- in diabolo means twice, polyaboloes with from 1 to 10 triangles are called respectively monoboloes, diaboloes, triaboloes, tetraboloes, pentaboloes, hexaboloes, heptaboloes, octaboloes, enneaboloes, and decaboloes.
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  • Polyabolo
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  • Polyabolo
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  • In recreational mathematics, a polyabolo (also known as a polytan) is a polyform with an isosceles right triangle as the base form. The name is a back formation from 'diabolo' although the shape formed by joining two triangles at just one vertex is not a proper polyabolo. On a false analogy as if di- in diabolo means twice, polyaboloes with from 1 to 10 triangles are called respectively monoboloes, diaboloes, triaboloes, tetraboloes, pentaboloes, hexaboloes, heptaboloes, octaboloes, enneaboloes, and decaboloes. There are two ways in which a square in a polyabolo can consist of two isosceles right triangles, but polyaboloes are considered equivalent if they have the same boundaries. The number of nonequivalent polyaboloes composed of 1, 2, 3, … triangles is 1, 3, 4, 14, 30, 107, 318, 1116, 3743, … (sequence A006074 in OEIS). Polyaboloes that are confined strictly to the plane and cannot be turned over may be termed one-sided. There are now four diaboloes (instead of three), six triaboloes (instead of four), 22 tetraboloes (instead of 14), and so on. A non-simply connected polyabolo is one that has one or more holes in it. The smallest value of n for which an n-abolo is non-simply connected is 7.
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