Zonish ball model
When I found George Hart's fascinating
fork
sculpture, I've wanted to reconstruct it. There is a
longer
description of the underlying desing, which says that it based on
a so-called zonish polyhedron.
On the surface of the sculpture pentagons and triangles were formed;
it was constructed from 240 forks. Each fork met four others: it went
below the ones at
the end, and above two other ones somewhere in the middle.
Based on this observation, the new construction should have
three-fold symmetry points at the vertices of a dodecahedron, and
five-fold symmetry points at the midpoints of its faces.
Trying several configurations those where midpoints of edges
were centers of rhombs whose sides were perpendicular to two triangles
and two pentagons seemed particularly appealing.
You can see these points - projected to the circumscribed sphere -
on the rotating picture. During the fine tuning,
lengths and other parameters have been chosen so that the
"necktie" along the
rhomb's side should be approximately symmetrical. Based on this computer
model, I've constructed the patterns. There are four kind of strips, 60 of each,
coming in two different lengths. On each sheet
you can find 30 strips, so you need
two sheets of each. Once the strips have been cut, you can glue them
together so that they overlap at the indicated positions.
The model was on display in one of CEU computer labs. The triangles
are bicolor: yellow in the outside, and white in the inside.
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