Question 20.35
5. Use the table of interior-angle measures from Exercise 4 to determine all the possible vertex types of regular polygons (with at most 12 sides) surrounding a point.
5.
The usual notation for a vertex type is to denote a regular -gon by , separate the sizes of polygons by periods, and list the polygons in clockwise order starting from the smallest number of sides, so that, for example, 3.3.3.3.3.3 denotes six equilateral triangles meeting at a vertex. The possible vertex types are 3.3.3.3.3.3, 3.3.3.3.6, 3.3.3.4.4, 3.3.4.3.4, 3.3.4.12, 3.4.3.12, 3.3.6.6, 3.6.3.6, 3.4.4.6, 3.4.6.4, 3.12.12, 4.4.4.4, 4.6.12, 4.8.8, 5.5.10, and 6.6.6.