I'm not feeling so well today, so here's some pictures from my recently-retired Art Book. This is a based on a photo of a c. 1420 CE floor marble tile design from a church, attributed to Uccello.
Here's another way to make pentagons. It can be adapted to inscribe any regular polygon within a circle; make n equal to the number of segments in line AB, draw a line from point C through the second point on line AB.
I should finish this... I thought it would be fun to make a design with a Middle-Eastern feel to it, the sort of design found in Islamic mosaic tile work.
Not a pentagon, but it is based on constructing squares within golden rectangles. I can't decide if this design would make a good alb or not.