We consider some miscellaneous questions regarding hedgehogs and their applications, beginning with convolution of hedgehogs. We study the generic singularities that occur during an eversion of the sphere following a generic path of hedgehogs and show that such a path necessarily includes hedgehogs carrying positive swallowtails. Finally, we show through an example that hedgehogs are not only a generalization of convex bodies, but also a way of thinking about convex hypersurfaces in conjunction with their spherical images. Our example consists in giving a set of conditions that is necessary and sufficient for the existence and uniqueness up to translations of a 3-dimensional polytope in \(\mathbb {R}^{3}\) having N facets with given unit outward normal vectors and corresponding facet parameters.