
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)
|