The Herschel nonahedron is a canonical polyhedron whose skeleton is the Herschel graph. It has 11 vertices, 18 edges, and 9 faces. Of the edges, 6 are short and 12 are long.
When the short edges are of unit length, the midsphere has midradius
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(1)
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As shown above, the 9 quadrilateral faces consist of 3 rhombi and 6 kites. The rhombi have edges of length
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(2)
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and angles
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(3)
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(4)
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while the kite edges are of length 1 and 
and have angles
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(5)
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(6)
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(7)
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A net for the solid consisting of faces with these dimensions is given above.
The Herschel enneahedron is implemented in the Wolfram Language as PolyhedronData["HerschelEnneahedron"].
