Three regular polygons, all with unit sides, share a common vertex and are all coplanar. Each polygon has a different number of sides, and each polygon shares a side with the other two; there are no gaps or overlaps. Find the number of sides for each polygon. There are multiple answers.

(In reply to re(2): solution by Tristan)

Tristan's comment brings out a point not noticed before, by Thalamus or me: each polygon has to have a different number of sides; so the three-hexagon solution doesn't count.  There are 8, rather than 9, non-degenerate solutions.

Posted by Charlie on 2004-07-12 22:06:48