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the area of 14 equilateral triangles. Its volume,{{r|berman}}
<math display=block>\frac{2\sqrt{2}+\sqrt{3}}{4}a^3\approx 1.140a^3,</math>
can be derived by slicing it into a central prism and three square pyramids, and adding their volumes.{{r|berman}}
It has the same [[Point groups in three dimensions|three-dimensional symmetry group]] as the triangular prism, the [[dihedral group]] <math>D_{3\mathrm{h}}</math> of order twelve. Its [[dihedral angle]]s can be calculated by adding the angles of the component pyramids and prism. The prism itself has square-triangle dihedral angles <math>\pi/2</math> and square-square angles <math>\pi/3</math>. The triangle-triangle angles on the pyramid are the same as in the [[regular octahedron]], and the square-triangle angles are half that. Therefore, for the triaugmented triangular prism, the dihedral angles incident to the degree-four vertices, on the edges of the prism triangles, and on the square-to-square prism edges are, respectively,{{r|johnson}}
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