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# Herschel Enneahedron

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

 (1)

As shown above, the 9 quadrilateral faces consist of 3 rhombi and 6 kites. The rhombi have edges of length

 (2)

and angles

 (3) (4)

while the kite edges are of length 1 and and have angles

 (5) (6) (7)

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"].

Enneahedron, Goldner-Harary Polyhedron

## Explore with Wolfram|Alpha

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## References

Hart, G. "Canonical Polyhedra." http://www.georgehart.com/virtual-polyhedra/canonical.html.

## Cite this as:

Weisstein, Eric W. "Herschel Enneahedron." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/HerschelEnneahedron.html