Construction of rhombic aproximate of Stewart toroid G3, together with construction of rhombic aproximate of tridiminished icosahedron (rhombic triacontahedron), shows that combination of these solids is equdecomposable with cube.
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The same is true for the icosahedron and drilled G3.
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So, the same is true for 3 icosahedra and drilled dodecahedron.
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References
[1] V.G. Boltjanskii, Tretja problema Hilberta, Nauka, Moskva 1977.
[2] I. Hafner, Live3D Animation to Solution of Conway-Radin-Sadun problem, Visual Mathematics Volume 9, No. 1, 2007
http://symmetry-us.com/Journals/visual40A/Visual40A.html
[3] Martin Kraus' Live3D applet http://www.vis.uni-stuttgart.de/~kraus/index.html