Question

Which of the following can be used to create a regular tessellation

check all that apple

a. equilateral triangle
b. regular hexagon
c. regular hexagon
d. square
e. regular octagon

Answer 1

• equilateral triangle
• square
• regular hexagon

Explanation:

The sum of the internal angles of a polygon with n sides is 180°·(n -2). Then the internal vertex angle will have measure ...

... internal angle = 180°·(n -2)/n

In order for the polygon to tile a plane, that angle must be a submultiple of 360°. That is, ...

... 360°/(internal angle)

must be an integer. Or, ...

... 360°/(180°(n -2)/n) = 2n/(n -2) . . . must be an integer

This is the case for n ∈ {3, 4, 6}, a regular triangle, square, and hexagon.