# Dehn Invariant of Some Disjoint Unions of Polyhedra with Icosahedral Symmetry

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Two sets and are equidecomposable (can be dissected into each other) if there are two families of sets and , , such that , the interiors of the are disjoint, , the interiors of the are disjoint, and is congruent to ). More intuitively, can be cut up into finitely many pieces that can be rearranged to form ; here the pieces should be polyhedra.

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Contributed by: Izidor Hafner (October 2014)

Open content licensed under CC BY-NC-SA

## Snapshots

## Details

That some combinations of Platonic and Archimedean solids have Dehn invariant 0 was shown in [1].

Reference

[1] J. H. Conway, C. Radin, and L. Sadun, "On Angles Whose Squared Trigonometric Functions Are Rational," *Discrete & Computational Geometry*, 22(3), 1999 pp. 321–332. doi:10.1007/PL00009463.

[2] N. Do, "Mathellaneous," *Gazette of the Australian Mathematical Society*, 33(2), 2006 pp. 81–87. www.austms.org.au/Publ/Gazette/2006/May06/mathellaneous.pdf.

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