what are the inner angles of a tetragonal trapezohedron I am making a 3D wooden lantern in the shape of a Tetragonal Trapezohedron. Think of a hollow Tetragonal Trapezohedron 3D object, where each face is a plank of wood. I am trying to determine the angles between the two planes, I should cut plank of wood at. For example the kite has the following dimensions, Short edge: 236 mm, Long edge: 403 mm. Face angles: 55°, 102°, 101°, 102°. The thickness of each face is 25 mm. I have tried cutting the long edges at 45° then taping them all together, but there is a gap, meaning that 45° is too large. The angle for the long edge should be less then 45°. How do you determine the angle between the long edges and the short edges?

This site (to which @Aretino already pointed) lists the dihedral angles as $105.14^\circ$, as illustrated below. (I verified that this angle is same at every edge.) So you should bevel at half this angle, $52.6^\circ$.

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![DihedralAng](
Side view illustrating the dihedral angle.

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![Upright](
Front view of Tetragonal Trapezohedron.

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