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The square gyrobicupola is a convex equilateral solid that is Johnson solid 
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The unit square 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 square orthobicupola, from which it differs only by the relative rotation of the top and bottom cupolas.
See also
Johnson Solid, Square Orthobicupola
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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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Cite this as:
Weisstein, Eric W. "Square Gyrobicupola." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/SquareGyrobicupola.html