Kurschak's Tile: A square, with an equilateral triangle drawn inwards on each side, the 8 intersections of the corresponding sides of adjacent triangles and the 4 mid-points of the new square formed by the free vertices of these triangles, These last 12 points form a regular dodecagon.

Kurschack's Theorem: A regular dodecagon inscribed in a unit circle has area 3.

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