Gerrymandering districts: Final Solution

The Washington Post had an article to today
about gerrymandering Ohio districts,

Ohio lawmakers, like those in nearly every state, use
detailed voting information to bunch their supporters
in often oddly shaped districts that promote the
reelection of incumbents and defeat of the other
party's candidates.

A simple geometric solution to gerrymandering
is this, pass a law that restricts district boundary's
to a polygon with no more than 5 points and
no interior angle greater than 180 degrees
(no angle bends back on itself).

The only two problems I could foresee is that
this is both simple and rational.