MathDB
there are exactly 29 non-similar regular n-pointed stars

Source: 2013 Saudi Arabia GMO TST I p3

July 26, 2020
combinatoricscombinatorial geometry

Problem Statement

Define a regular nn-pointed star to be a union of nn lines segments P1P2,P2P3,...,PnP1P_1P_2, P_2P_3, ..., P_nP_1 such that ∙\bullet the points P1,P2,...,PnP_1,P_2,...,P_n are coplanar and no three of them are collinear, ∙\bullet each of the nn line segments intersects at least one of the other line segments at a point other than an endpoint, ∙\bullet all of the angles at P1,P2,...,PnP_1, P_2,..., P_n are congruent , ∙\bullet all of the nn line segments P1P2,P2P3,...,PnP1P_1P_2, P_2P_3, ..., P_nP_1 are congruent, and ∙\bullet the path P1P2...PnP1P_1P_2...P_nP_1 turns counterclockwise at an angle less than 180o180^o at each vertex. There are no regular 33-pointed, 44-pointed, or 66-pointed stars. All regular 55-pointed star are similar, but there are two non-similar regular 77-pointed stars. Find all possible values of nn such that there are exactly 2929 non-similar regular nn-pointed stars.
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