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The metabigyrate rhombicosidodecahedron is a convex equilateral solid obtained by rotating two of the pentagonal cupolas of a small
rhombicosidodecahedron located in the "meta" (in the chemical arene
substitution pattern sense) by 1/10 of a turn each. It is Johnson
solid 
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The unit metabigyrate rhombicosidodecahedron has volume
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(1)
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and Dehn invariant
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(2)
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(3)
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where the first expression uses the basis of Conway et al. (1999). It can be dissected into the gryrate rhombicosidodecahedron, parabigyrate rhombicosidodecahedron, small rhombicosidodecahedron, and trigyrate rhombicosidodecahedron (E. Weisstein, Aug. 17, 2023).
