Stephanoid

A stephanoid or crown polyhedron is a noble polyhedron whose faces are butterflies and which has dihedral symmetry. Their convex hulls are prisms or antiprisms. They are self-dual.

There is a stephanoid with $$n$$-gonal dihedral symmetry for every pair $$a$$ and $$b$$ where the faces have vertices $$a$$ steps apart on one base and $$b$$ steps apart on the other base, where $$a \neq b$$ and $$a + b \neq n$$ (those cases are degenerate). This gives $$\left\lfloor\tfrac{n-2}2\right\rfloor\left\lceil\tfrac{n-2}2\right\rceil$$ distinct $$n$$-gonal stephanoids.