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Elongated Triangular Gyrobicupola

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J36
J36Net

The elongated triangular gyrobicupola is a convex equilateral solid that is Johnson solid J_(36).

The unit elongated triangular gyrobicupola has volume

V=5/3sqrt(2)+3/2sqrt(3)
(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 elongated triangular orthobicupola, from which it differs only by relative rotation of the top and bottom cupolas.

See also

Johnson Solid, Triangular Gyrobicupola

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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 Triangular Gyrobicupola." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/ElongatedTriangularGyrobicupola.html

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