Ring of 2n Rhombohedra

number of rhombohedra

10

separate halves

opacity tetrahedron

opacity octahedron

Rings are formed by face-to-face connections of

2n

rhombohedra, where

n=2,3,4,...

. 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

2

cos

π

n

csc

π

n

, giving the series 0.707107, 1., 1.30656, 1.61803, 1.93185, 2.24698, …. If

n=2

, the ratio is

1

2

, producing an oblate silver rhombohedron. The first member of this family of rhombohedral rings is the rhombic dodecahedron, composed of

2×2=4

oblate silver rhombohedra. A cube and a prolate golden rhombohedron are obtained when

n=3

and

5.