The tetragonal trapezohedron is the dual of the square antiprism. For a square antiprism with unit edge lengths, the edge lengths of the corresponding tetragonal trapezohedron are
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(1)
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(2)
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and the corresponding surface area and volume are
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(3)
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(4)
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The skeleton of the tetragonal trapezohedron is a non-cubic graph (it has degree sequence (3, 3, 3, 3, 3, 3, 3, 3, 4, 4)) in which all faces touch an even number of sides but the graph is not three-colorable.
