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Elongated Pentagonal Gyrobicupola

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J39
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The elongated pentagonal gyrobicupola is a convex equilateral solid that is Johnson solid J_(39).

The unit elongated pentagonal gyrobicupola has volume

V=1/6(10+8sqrt(5)+15sqrt(5+2sqrt(5)))
(1)

and Dehn invariant

D=30<3>_5-5<5>_1
(2)
=-5[-3cot^(-1)(2/(sqrt(5)))+tan^(-1)2],
(3)

where the first expression uses the basis of Conway et al. (1999). It can be dissected into the elongated pentagonal orthobicupola, from which it differs only by a relative rotate of top and bottom cupolas with repsect to one another.

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. "Elongated Pentagonal Gyrobicupola." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/ElongatedPentagonalGyrobicupola.html

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