A semiregular tiling has two regular octagons and one regular p-gon at each vertex. What is p?
A) 3
B) 4
C) 5
D) 6

Question

Quizplus · Accepted Answer

In a semiregular tiling, the sum of the interior angles at each vertex must be 360 degrees. The interior angle of a regular octagon is 135 degrees. Two octagons contribute 2 * 135 = 270 degrees. Therefore, the remaining angle must be 360 - 270 = 90 degrees, which corresponds to a square (p = 4).

A Semiregular Tiling Has Two Regular Octagons and One Regular