Skewered cube: the petal explorer

A unit cube has a rigid axle through it, pinned to the plane at a point P a distance a from where the axle exits the cube. As the cube rocks on the pivot, only its edges touch the ground, tracing a path made of alternating radii from P. The shape depends on which line through the cube the axle follows — pick one below, then drag the axle length to watch the path unfold.

a = 0.610