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Pentagonal Gyrobicupola

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The pentagonal gyrobicupola is a convex equilateral solid that is Johnson solid J_(31).

The unit pentagonal gyrobicupola has volume

V=1/3(5+4sqrt(5))
(1)

and Dehn invariant

D=-15<3>_5+(25)/2<5>_1
(2)
=5/2[-3cot^(-1)(2/(sqrt(5)))+5tan^(-1)2],
(3)

where the first expression uses the basis of Conway et al. (1999). It can be dissected into the pentagonal orthobicupola, from which it differs only by the relative rotation of the top and bottom cupolas.

See also

Diminished Polyhedron, Small Rhombicosidodecahedron

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References

Conway, J. H.; Radin, C.; and Sadun, L. "On Angles Whose Squared Trigonometric Functions Are Rational." Discr. Computat. Geom. 22, 321-332, 1999.Johnson, N. W. "Convex Polyhedra with Regular Faces." Canad. J. Math. 18, 169-200, 1966.

Cite this as:

Weisstein, Eric W. "Pentagonal Gyrobicupola." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/PentagonalGyrobicupola.html

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