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Herschel Enneahedron


HerschelEnneahedron

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.

HerschelEnneahedronMidpshere

When the short edges are of unit length, the midsphere has midradius

 rho=sqrt((111sqrt(17))/(128)-(249)/(128)).
(1)
HerschelEnneahedronFaces

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

 a=3/8(sqrt(17)+1)=1.9211...
(2)

and angles

theta_1=cos^(-1)((5-sqrt(17))/2)
(3)
theta_2=cos^(-1)((sqrt(17)-5)/2),
(4)

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

phi_1=cos^(-1)((9sqrt(17)-79)/(128))
(5)
phi_2=cos^(-1)((sqrt(17)-7)/(16))
(6)
phi_3=cos^(-1)((sqrt(17)+1)/8).
(7)
HerschelEnneahedronNet

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"].


See also

Enneahedron, Goldner-Harary Polyhedron

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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

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