At first blush, this looks like a tessellation using regular 5-gons, 6-gons, 7-gons and 8-gons. However, things are not always what they seem.

1. Show that it is not in fact possible for all the polygons to be regular.

2. Assuming that all polygons with the same number of sides are congruent, what is the greatest number of types of polygon which can be regular?

Design taken from Altair Designs by Ensor Holliday