I'm so confused now
I was using sheldon's calculator, I was usning another one and came out with different figures too
that is one difference, you said you ordered custom from Peter, that is why you got a 56, mine came with the stock 52
as far as the 406 as 20 I don't know, I am new to all these smaller tires
20" tires come in 2 flavors. The 451 size is a taller and skinnier version of the BMX (406) size. Tires and rims are not interchangeable. The 451 size is usually lighter and faster. The wider BMX size is more designed for touring and commuting.
http://www.sheldonbrown.com/gears/
Sheldon Brown's Bicycle Gear Calculator