# Octagon Curiousities

Construct squares on the sides (exterior or interior) on an octagon. Construct segments connecting the centers of opposite squares. The midpoints of these segments form the vertices of a quadrilateral that is both equidiagonal and orthodiagonal.

Construct an octagon from the midpoints of the sides of another octagon. Build squares on this midpoint octagon as above. The midpoints of the segments connecting the centers of opposite squares form the vertices of a square.

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