The Goldner-Harary polyhedron is the term given in this work to the polyhedral embedding of the Goldner-Harary graph. This solid is an augmented triangular dipyramid, a construction described by Grünbaum (2003, p. 357), though without identification of the particular resulting solid or skeleton. It has 11 vertices, 27 edges, and 18 faces.
As a canonical polyhedron with unit midradius, its edges are of four different lengths,
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(1)
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(2)
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(3)
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(4)
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with tallies of 6, 12, 6, and 3 respectively.
The canonical Goldner-Harary polyhedron has surface area and volume given by
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(5)
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(6)
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Its net is illustrated above.
The Goldner-Harary polyhedron is also the polyhedron dual of the truncated triangular prism, as illustrated above for the canonical versions of these solids.
