TOPICS
Search

Pentagonal Orthocupolarotunda

DOWNLOAD Mathematica NotebookDownload Wolfram Notebook
J32
J32Net

The pentagonal orthocupolarotunda is a convex equilateral solid that is Johnson solid J_(32).

The unit pentagonal orthocupolarotunda has volume

V=1/(12)(55+25sqrt(5)),
(1)

and Dehn invariant

D=-15<3>_5+(25)/2<5>_1
(2)
=5/2[-3cot^(-1)(2/(sqrt(5)))+5tan^(-1)2],
(3)

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

See also

Diminished Polyhedron, Small Rhombicosidodecahedron

Explore with Wolfram|Alpha

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.

Referenced on Wolfram|Alpha

Pentagonal Orthocupolarotunda

Cite this as:

Weisstein, Eric W. "Pentagonal Orthocupolarotunda." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/PentagonalOrthocupolarotunda.html

Subject classifications