Another Dissection of Two Rhombic Solids into an Icosidodecahedron and a Rhombicosidodecahedron

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This Demonstration gives a dissection of the rhombic 120-hedron and a rhombic-like solid that consists of 30 halves of the rhombic dodecahedron of the second kind put on the faces of a certain rhombic solid; the result is a combination of the icosidodecahedron and the rhombicosidodecahedron .

Contributed by: Izidor Hafner (March 2011)
Open content licensed under CC BY-NC-SA



That such dissections exist follows from [1], where it is shown that certain combinations of Platonic and Archimedean solids have Dehn invariant 0. This Demonstration uses the longer diagonal of the golden rhombus, while the Demonstration in the related links uses the shorter diagonal.

[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.

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