Polyhedra

There are 5 regular polyhedra - tetrahedron, hexahedron (cube), octahedron, dodecahedron and icosahedron.

There is also a curious way that these 3-dimensional objects fit together. Starting with a dodecahedron, fit around an icosahedron, so that the 20 vertices of the dodecahedron meet the centre of the 20 faces of the icosahedron. Then build an octahedron around the icosahedron so that the 12 vertices of the icosahedron meet with the 12 edges of the octahedron (according to the golden section). Next build a tetrahedron around the octahedron so that the 6 vertices of the octahedron meet with the mid points of the 6 edges of the tetrahedron. Finally put a cube around the tetrahedron so that the corners meet.

Assuming that all 30 edges of the dodecahedron are 2 in length, and that all of the polyhedra are regular. What is the length of the cube's edge?




Edit [Moderator]: Moved from Riddles to Science & Mathematics.