You could try to duplicate the basic angles of the rug.
The skinny solid color diamond looks like the angles might be 30-150-30-150 degrees.
The patterned diamonds/slanted squares look like their angles might be 75-105-75-105 degrees.
The tumbling blocks assembly technique could be adapted to these angles.
(Someone might want to check out the numbers - I think they are right - but they may not be)
It is rewarding to find a use for that old geometry class!