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Square Gyrobicupola

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J29
J29Net

The square gyrobicupola is a convex equilateral solid that is Johnson solid J_(29).

The unit square gyrobicupola has volume

V=2+4/3sqrt(2)
(1)

and Dehn invariant

D=24<3>_2
(2)
=24tan^(-1)(sqrt(2)),
(3)

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.

Cite this as:

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

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