What kinds of regular polygons can be used for regular tessellations?

3

Equilateral triangles, squares and regular hexagons are the only regular polygons that tessellate.

Step-by-step explanation:

In mathematics, a tessellation is the covering of the plane by closed geometric shapes, called tiles, without gaps or overlaps. Regular polygons have congruent straight sides. When we slide or rotate a regular polygon, the side of the original figure and the side of its translation will match.

Equilateral triangles, squares and regular hexagons are the only regular polygons that tessellate. Therefore, there are only three regular tessellations.

check the picture below.

well, the angle at the vertex d is clearly not a right-angle, let's check for the one at the vertex f which does look like,   however if it's indeed, that means ef is perpendicular to df, in which case their slopes will be negative reciprocal of each other.

so the negative reciprocal of the slope of ef is 1, however the slope of df is not 1, is 1/2, so nope, they're not perpendicular lines.