Regular dodecagons (12-gons) and equilateral triangles can form a tiling of the plane that has at every vertex:
A) two dodecagons and two triangles.
B) two dodecagons and one triangle.
C) one dodecagon and two triangles.
D) one dodecagon and three triangles.

Question

Quizplus · Accepted Answer

In this tiling pattern, each vertex is shared by two dodecagons and one equilateral triangle. This can be observed by noticing that three triangles add up to 360 degrees (the same as the interior angle of a dodecagon) and therefore fit perfectly around the vertex with two adjacent dodecagons. Therefore, the correct choice is B - two dodecagons and one triangle.

Regular Dodecagons (12-Gons) and Equilateral Triangles Can Form a Tiling