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There cannot be an obtuse equilateral triangle.

A rhombus is an equilateral quadrilateral with two obtuse angles (and two acute ones). Not sure if that counts as an obtuse equilateral.

All regular polygons with more than four sides will be obtuse and equilateral. There are also other polygons that will meet these requirements. These will be squashed polygons in the same way that a rhombus is a squashed square.

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Q: What does an obtuse equilateral look like?
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