**Theorem 3.4**: If k < n/2, then in an {n/k} star there are
1 + nk - n regions. They consist of

1 regular convex n-gon, and

if k > 1, there will be n triangles, and

n(k - 2) quadrilaterals.

**proof**: First note that the {n/1} star in the center of the
figure is a regular convex n-gon. Next, note that all the other
regions have a uniquely determined extreme vertex point which is a
point of one of the {n/j} stars, j = 2, . . . , k, so there will be a
one to one correspondence between the points which are not on the
convex n-gon and the other regions. The points of the {n/2} star will
be vertices of triangles each of whose base is a side in the convex
n-gon, so there will be n triangles. The other points will be
vertices of {n/j} stars where j > 2. The base of each of those
regions will be an angle between the points of the {n/j-1}. As a
result each of those regions will be quadrilaterals.