To construct as regular 13-gon:

 

Draw a circle and a radius (MN).

Trisect the radius (points O and P do this).

Trisect the middle (OP) of the trisecting segments. (Points Q and R do this).

Trisect Segment QR.

Using the points that trisect QR and N, draw a circle as shown with that radius.

Using that, work around the circle.

Connect the points (not shown) to make a regular 13-gon.

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