  Recently we have shown that for $2+1-$dimensional thin-shell wormholes a
non-circular throat may lead to a physical wormhole in the sense that the
energy conditions are satisfied. By the same token, herein we consider angular
dependent throat geometry embedded in a $2+1-$dimensional flat spacetime in
polar coordinates. It is shown that a generic, natural example of throat
geometry is provided remarkably by a hypocycloid. That is, two flat
$2+1-$dimensions are glued together along a hypocycloid. The energy required in
each hypocycloid increases with the frequency of the roller circle inside the
large one.
