Cube 10-Compound

A cube 10-compound by be obtained by beginning with an initial cube and rotating it by an angle about the axis, then adding a second cube obtained by rotating the first by an angle about the axis, where is the golden ratio.

It is implemented in the Wolfram Language as PolyhedronData["CubeTenCompound"].

The angle places corresponding faces of first two cubes in a symmetrical position relative to one another, and makes each of these faces cut the other in an isosceles right triangle. The remaining eight cubes of the compound are then generating by adding four more pairs of cubes rotated by angles about the axis (the same rotations used to construct the cube 5-compound) for , 2, 3, 4.

A net for constructing the solid is illustrated above. The edge lengths are given by

			(1)
			(2)
			(3)
			(4)
			(5)
			(6)
			(7)
			(8)
			(9)
			(10)
			(11)
			(12)
			(13)

where indicated a polynomial root.

The surface area of the solid is

			(14)
			(15)