A self-inverse chord is a chord that has the same intervallic structure of its inverse, where a generic inversion is defined as the product of a do-based inversion (i.e. mirror reflection through the axis keeping fixed the pitch-integers 0 and 6) and a transposition.

The n-circle box shows 5 of the 10 possible self-inverse heptachords (up to transposition!). Note that you will have no solutions at all if you are asking for more than 10 solutions.