When four polygons, an a-gon, a b-gon, a c-gon, and a d-gon, surround a point, it can be...

When four polygons, an a-gon, a b-gon, a c-gon, and a d-gon, surround a point, it can be shown that the following equation is satisfied:

a. Find four combinations of whole numbers that satisfy this equation.

b. One of the combinations from part (a) gives a regular tiling. Which one is it?

c. The remaining three combinations from part (a) can each surround a vertex in two different ways. Of those six arrangements, four cannot be extended to a semiregular tiling. Which are they?

d. The remaining two arrangements from part (c) can be extended to a semiregular tiling. Which are they?