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Parabiaugmented Dodecahedron

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The parabiaugmented dodecahedron is a convex equilateral solid that is Johnson solid J_(60).

The unit parabiaugmented dodecahedron has volume

V=1/6(25+11sqrt(5))
(1)

and Dehn invariant

D=30<3>_5-35<5>_1
(2)
=5[3cot^(-1)(2/(sqrt(5)))-7tan^(-1)2],
(3)

where the first expression uses the basis of Conway et al. (1999). It can be dissected into the metabiaugmented dodecahedron, from which it differs only by the relative positions of the two augmented pentagonal pyramids.

See also

Augmentation, Regular Dodecahedron

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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.

Referenced on Wolfram|Alpha

Parabiaugmented Dodecahedron

Cite this as:

Weisstein, Eric W. "Parabiaugmented Dodecahedron." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/ParabiaugmentedDodecahedron.html

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