Generating an octagon - Colegiul Național din Iași (Iași - Roumanie) Colegiul Național Andrei Șaguna (Brașov)

Staring with the midpoints of a square we can generate an octagon with the two opposites vertices of the square. Generalisations: if we replace the square with any other paralelogram or instead of midpoints considering different ratio points on the side of the square.