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The pentagonal orthobirotunda is a convex equilateral orthobirotunda having regular pentagonal upper and lower faces arranged symmetrically about the
midplane. It is Johnson solid 
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The unit pentagonal orthobirotunda 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 regular icosidodecahedron, from which it differs only by the relative rotation of the top and bottom rotundas.
