Geodesic
A short proof of the twelve-point theorem
Matematičeskie zametki, Tome 77 (2005) no. 1, pp. 117-120

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We present a short elementary proof of the following twelve-point theorem. Let $M$ be a convex polygon with vertices at lattice points, containing a single lattice point in its interior. Denote by $m$ (respectively, $m^*$) the number of lattice points in the boundary of $M$ (respectively, in the boundary of the dual polygon). Then $m+m^*=12$. 
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     title = {A short proof of the twelve-point theorem},
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D. Repovš; M. B. Skopenkov; M. Cencelj. A short proof of the twelve-point theorem. Matematičeskie zametki, Tome 77 (2005) no. 1, pp. 117-120. http://geodesic.mathdoc.fr/item/MZM_2005_77_1_a9/