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 s_1 | = | sqrt(sqrt(2) - 1) s_2 | = | sqrt(1/2 + 1/sqrt(2)), and the corresponding surface area and volume are S | = | 2sqrt(2 + 4sqrt(2)) V | = | 1/3 sqrt(4 + 3sqrt(2)).
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