Which of the following types of regular n-gons will form tessellations of the plane by themselves?

Question

3-gons
6-gons
8-gons
or which two?

Answer 1

3-gons and 6-gons.

The angle between sides of a regular n-gon is:

180 - 360/n

If this is evenly divisible by 360, then you can tessalate the
n-gon.

3-gon
180 - 360/3 = 180 - 120 = 60
360/60 = 6

A 3-gon (equilateral triangle) can be tesselated with 6 triangles meeting at each vertex.
________________

6-gon
180 - 360/6 = 180 - 60 = 120
360/120 = 3

A 6-gon (regular hexagon) can be tesselated with 3 hexagons meeting at each vertex.
___________

8-gon
180 - 360/8 = 180 - 45 = 135
360/135 = 8/3

This is not an integer. An octagon cannot be tesselated.