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Metabiaugmented Truncated Dodecahedron

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J70
J70Net

The metabiaugmented truncated dodecahedron is a convex equilateral solid that is Johnson solid J_(70).

The unit metabiaugmented 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 parabiaugmented 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. "Metabiaugmented Truncated Dodecahedron." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/MetabiaugmentedTruncatedDodecahedron.html

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