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Dissection of Two Rhombic Solids into an Icosidodecahedron and a Rhomb-Icosi-Dodecahedron

This Demonstration gives a dissection of the rhombic hexecontahedron and of a rhombic-like solid that consists of 30 halves of the rhombic dodecahedron of the second kind put on a triacontahedron; the result is a combination of the icosidodecahedron and the rhomb-icosi-dodecahedron.

Contributed by: Izidor Hafner

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(Over 500 lines omitted)

That such dissections exist follows from [1], where it is shown that certain combinations of Platonic and Archimedean solids have Dehn invariant 0.

[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.

Dehn Invariant (Wolfram MathWorld)

Dissection (Wolfram MathWorld)

Hexecontahedron (Wolfram MathWorld)

Icosidodecahedron (Wolfram MathWorld)

Triacontahedron (Wolfram MathWorld)

"Dissection of Two Rhombic Solids into an Icosidodecahedron and a Rhomb-Icosi-Dodecahedron" from The Wolfram Demonstrations Project
http://demonstrations.wolfram.com/DissectionOfTwoRhombicSolidsIntoAnIcosidodecahedronAndARhomb/

Contributed by: Izidor Hafner

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