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Decomposition into Isosceles Triangles with Angles That Are Multiples of Pi/4

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Figures such as a square, an octagon, or an octagram can be dissected into isosceles triangles where all three angles are multiples of
π/4
. Such triangles have the same role as iso-penta triangles for five-fold symmetry. The figures in this Demonstration are not always decomposed into triangles; sometimes squares and rhombuses, which can be divided along a diagonal into two such triangles, are left whole.
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