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).
It is a self-dual polyhedron.
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
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(1)
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(2)
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(3)
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(4)
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(5)
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For the polyhedron with unit midradius, the side lengths are
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(6)
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(7)
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(8)
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and the generalized diameter, surface area, and volume are
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(9)
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(10)
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(11)
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A net for the polyhedron is illustrated above.
