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Parabiaugmented Truncated Dodecahedron

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J69
J69Net

The parabiaugmented truncated dodecahedron is a convex equilateral solid that is Johnson solid J_(69).

The unit parabiaugmented truncated dodecahedron has volume

V=1/(12)(515+251sqrt(5))
(1)

and Dehn invariant

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

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

See also

Augmentation, Truncated 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.

Cite this as:

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

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