Hexadecagon
Coxeter states that every parallel-sided 2m-gon can be divided into m(m-1)/2 rhombs. For the regular hexadecagon, m=8, and it can be divided into 28: 4 squares and 3 sets of 8 rhombs. This decomposition is based on a Petrie polygon projection of a 8-cube, with 28 of 1792 faces.  The list A006245 enumerates the number of solutions as 1232944, including up to 16-fold rotations and chiral forms in reflection.