# Origami Variations

These are also pictures of models from the origami display that I installed in the
Amherst College Mathematics
and Computer Science Department in 1995.
However, these models were removed a couple of years after the original installation
and before I took any photographs.

## Variations on a Theme

The model in the back right corner of the first photograph is a black cube
intersecting a white octahedron. This is one of three possible
intersecting Platonic dual solids described
elsewhere in these pages.
The rest of the models below are variations on this geometric theme, all from
various books of
Tomoko Fuse.

Another variation on the cube/octahedron duality theme. In this sequence,
which was first introduced to me by Sanford Whiteman (Amherst College '93),
a framework octahedron assembled from six waterbomb bases gradually morphs
into a framework cube.

## The Serendipity of Origami

While origami is beautiful and versatile art form, it does have its shortcomings
as a means to represent polyhedral forms. For example, if you
compare the
hanging models from the principal exhibit
with the polyhedra they represent, you see
that the origami models that contain pentagons and hexagons either use
support struts to divide these polygons
into triangles or are unstable enough to warp easily.

However, there are some cases in which the origami modules themselves cast light
on polyhedral relationships. If you try to make a tetrahedron out of Tomoko Fuse's
*Plain Open Frame Unit* (the unit used for six of the nine hanging solids),
the normally angled modules lie flat and
you get the model on the left of the photographs below, which is a cube
with three corners removed. This coincidence reflects the intimate connections between
the tetrahedron, octahedron, and cube described
here and
here.
A simple variation in creases gives the model on the right, which (with
the eight triangular sides filled in) is a cuboctahedron.

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