Small supersemicupola

The small supersemicupola is the first known example of a 7-7-3 acrohedron, i.e. a polyhedron with all regular faces that has two heptagons and a triangle meeting at a vertex. It was discovered by Mason Green in 2005 along with the great supersemicupola, a 7/2-7/2-3 acrohedron. Most acrons containing heptagons have no known acrohedron, so the existence of a 7-7-3 acrohedron is rather unusual.

As the name suggests, the small supersemicupola bears similarities to a heptagrammic semicupola (cuploid). Like the semicupolae, it is non-orientable.

The shape is part of a larger family of regular-faced polyhedra formed using what McNeill calls "Green's Rules". Using Green's Rules, $n$-$n$-3 acrohedra can be produced for $n$ = 4, 5, 6, 7, 8, 10, 5/2, 7/2, 8/3, and 10/3. All are orbiform.