9 Lattice-Point Polygons

9.1 Regular polygons in the integer lattice

Consider a regular square lattice, the integer lattice, the intersection points formed by a

grid of uniformly spaced parallel horizontal and vertical lines in the plane. One may easily

find vertex points in that lattice that form the vertices of various larger squares. What other

types of regular polygons we might find in this lattice?

Question 69. Can one find vertex points in the integer lattice that form the vertices of a

regular hexagon? Or a regular pentagon? An equilateral triangle? Which regular polygons

can be found in the integer lattice?

Go ahead and try! Which regular polygons can you find?