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

Question

Quizplus · Accepted Answer

A semiregular tiling with four equilateral triangles and one p-gon at each vertex must satisfy the angle sum around a vertex being 360 degrees. Each equilateral triangle has an angle of 60 degrees, so four triangles contribute 240 degrees. The remaining angle must be 120 degrees, which corresponds to a regular hexagon (6-gon).

A Semiregular Tiling Has Four Equilateral Triangles and One P-Gon