what are the inner angles of a tetragonal trapezohedron

Question

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?

Answer 1

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, $52.6^\circ$.

---

         
          ^{Side view illustrating the dihedral angle.}

---

         
          ^{Front view of Tetragonal Trapezohedron.}

---