Compound of 15 Golden Rectangles
This is a quick 3D "doodle" of sorts, in the form of 15 rectangles. One
way to make a compound of 15 rectangles is just to connect all fifteen opposite
pairs of edges of an icosahedron. This image shows three pairs connected:
But in the Zome construction at the top of the page, the ratio "goes the
other way." You can think of it as re-proportioning those icosahedron
rectangles from 1-by-tau to tau-by-1. Or equivalently,
you can rotate each rectangle 90 degrees about the icosahedron's 2-fold axis
that goes through its pair of opposite edges. In the model illustrated, each
is a golden rectancle of size 2b3 by 2b4. In order to have balls at the crossing points, the long sides are built as b3+b2+b2+b3 and the short sides are b1+b2+b2+b1. To build it, you can start with a 2b2
icosahedron. Opposite pairs of icosahedron edges are the middle portions
of the long sides of the rectangles, so extend them with a b3 in each direction
to complete the long sides. The image below shows the view down a 5-fold
axis of the compound.
