Mary asked a question about doubles which prompted me to post. Since doubles and polys are close to my heart, here's some info. Please add/correct if you can.
David Kirchhoff taught me early on that tepals (petals and sepals) are formed in whorls at the base of a bloom. Single blooms have two whorls, an inner with 3 petals and an outer with 3 sepals. There are 2 basic forms of doubles, petaloid and layered/hose-in-hose. The petaloid have the normal two whorls, but some or all of the stamen have been converted into extra "petals". Layered doubles have extra sets of whorls with tepals stacked on top of each other. The following are examples of the two types; Barry Goldwater and Amanda's Little Red Shoes.
Polymerous daylilies have two whorls but extra tepals on each plus a stamen for each tepal. One can tell whether a bloom is fused or poly by counting the stamen. A 4x4 poly will have 8 stamen, a 5x5 will have 10 and a 6x6 will have 12, etc.
The last did have 12 stamen but I pulled a few to hybridize with.