Icosagon
Coxeter states that every parallel-sided 2m-gon can be divided into m(m-1)/2 rhombs. For the icosagon, m=10, and it can be divided into 45: 5 squares and 4 sets of 10 rhombs. This decomposition is based on a Petrie polygon projection of a 10-cube, with 45 of 11520 faces.  The list A006245 enumerates the number of solutions as 18,410,581,880, including up to 20-fold rotations and chiral forms in reflection.