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Elongated Pentagonal Orthobirotunda


J42J42Net

The elongated pentagonal orthobirotunda is a convex equilateral orthobirotunda having regular pentagonal upper and lower rotundas arranged symmetrically with respect to each other and separated by a vertical strip of squares. It is Johnson solid J_(42).

The unit elongated pentagonal orthobirotunda has volume

 V=1/6(45+17sqrt(5)+15sqrt(5+2sqrt(5)))
(1)

and Dehn invariant

D=-60<3>_5+30<5>_1
(2)
=-30sin^(-1)((5-4sqrt(5))/(15)),
(3)

where the first expression uses the basis of Conway et al. (1999). It can be dissected into the elongated pentagonal gyrobirotunda, from which it differs only by relative rotation of the top and bottom rotundas.


See also

Birotunda, Johnson Solid, Orthobirotuna

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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 Orthobirotunda." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/ElongatedPentagonalOrthobirotunda.html

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