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The elongated pentagonal gyrobicupola is a convex equilateral solid that is Johnson solid 
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The unit elongated pentagonal gyrobicupola has volume
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(1) |
and Dehn invariant
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.
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Elongated Pentagonal Gyrobicupola
Cite this as:
Weisstein, Eric W. "Elongated Pentagonal Gyrobicupola." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/ElongatedPentagonalGyrobicupola.html