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Metabiaugmented Hexagonal Prism

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J56
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The metabiaugmented hexagonal prism is a convex equilateral solid that is Johnson solid J_(56).

The metabiaugmented hexagonal prism has volume

V=1/6(2sqrt(2)+9sqrt(3))
(1)

and Dehn invariant

D=24<3>_2
(2)
=24tan^(-1)(sqrt(2)),
(3)

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

See also

Augmentation, Hexagonal Prism, Johnson Solid

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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 Hexagonal Prism." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/MetabiaugmentedHexagonalPrism.html

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