The polyhedron compound of the truncated icosahedron and its dual, the pentakis dodecahedron. The compound can be constructed from a truncated icosahedron of unit edge length by midpoint augmentation with heights
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(1)
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(2)
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The resulting solid has edge lengths
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(3)
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(4)
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(5)
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(6)
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(7)
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(8)
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surface area 
given by the fourth largest positive root of
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(9)
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and volume
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(10)
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