KGS math club/solution 11 1

There are six ways:

1. the vertices of a square
2. the vertices of a 60-degree rhombus
3. the vertices of an equlateral triangle, plus its midpoint
4. the vertices of an equlateral triangle, plus a point on a symmetry axis that is a side-length away from the vertex through which that axis passes
5. the vertices of an equlateral triangle, plus a point on a symmetry axis that is a side-length away, in the opposite direction, from the vertex through which that axis passes
6. Four of the vertices of a regular pentagon