Ring of 2n Rhombohedra
Ring of 2n Rhombohedra
Rings are formed by face-to-face connections of rhombohedra, where . Each rhombohedron is made up of two congruent tetrahedral parts and one octahedral part at the center. The diagonal ratio of the faces of the rhombohedra is csc, giving the series 0.707107, 1., 1.30656, 1.61803, 1.93185, 2.24698, …. If , the ratio is , producing an oblate silver rhombohedron. The first member of this family of rhombohedral rings is the rhombic dodecahedron, composed of oblate silver rhombohedra. A cube and a prolate golden rhombohedron are obtained when and
2n
n=2,3,4,...
2
cos
π
n
π
n
n=2
1
2
2×2=4
n=3
5.