The Goddard-Henning enneahedron, a term coined here, is the canonical polyhedron obtained from the Goddard-Henning
graph. It has 9 vertices, 16 edges (consisting of 3 distinct edge lengths), and
9 faces (consisting of 3 distinct face types).

In particular, the bottom face is a square, the four faces sharing an edge with the bottom are isosceles triangles,
and the remaining four faces that meet at the apex are kites.
The face angles as shown are

(1)

(2)

(3)

(4)

(5)

For the polyhedron with unit midradius, the side lengths
are