Three Interpenetrating Golden Bricks

perforate bricks

0.618

perforate icosahedron

0.8

compress

1

expand

1

icosahedron

dodecahedron

Each of three mutually perpendicular bricks have sides

a

,

b

,

c

such that

a/b=b/c=ϕ

, where

ϕ

is the golden ratio. Each face is perforated again with sides in the proportion of the golden ratio.

The bricks are fit tightly together as a Borromean ring. When they are compressed, the vertices of the resulting golden rectangles coincide with the vertices of an icosahedron. When the golden rectangles are extended until equal to the square of the golden ratio, the edges coincide with the edges of a dodecahedron.