Hypocycloidal throat for 2+1-dimensional thin-shell wormholes

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 an angular dependent throat geometry embedded in a 2 + 1-dimensional flat spacetime in polar coordinates. It is shown that, remarkably, a generic, natural example of the throat geometry is provided 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.