Symmetric Compositions of Rhombic Dodecahedra of the Second Kind

show rhombic dodecahedron

move apart

symmetry type

D2

C2v

C3v

C5v

D5

number of parts

opacity

This Demonstration shows some symmetric compositions of rhombic dodecahedra of the second kind.

It also shows that a rhombic dodecahedron of the second kind consists of two prolate and two oblate golden rhombohedra. The ratio of the diagonals

d

2

/

d

1

is the golden ratio

τ

, and the same is true for the ratio of the volumes of the rhombohedra. The area of the rhombus is

d

1

d

2

/2

. The volume of the dodecahedron is

3

d

2

2

.