icosahedron-edge

3D Model

A regular icosahedron may be dissected into 30 identical pieces, each containing one edge of the icosahedron. The pieces look like this.

Apart from the single dihedral angle corresponding to the edge of the icosahedron, all the other dihedral angles are rational: 72°, 90°, or 120°.

Since it’s possible to create a single-angle polyhedron for any rational angle, that means we can use this as a building block to create a single-angle polyhedron whose only non-right-angled edge has a dihedral angle of arccos(-√5 / 3).