Platonic Love
There are only five regular solids in the universe: tetrahedron,
cube, octahedron, dodecahedron and icosahedron. The first known
description of these solids is found in the writings of Plato, hence
the name “Platonic solids”. They all have a “neat”
structure: they can all be inscribed within a sphere, and in each
solid, all planes, edges and vertices are of the same size. This
unique regularity may have inspired Plato to attribute a cosmological
significance to these solids: he associated four of the solids with
the four elements, while, in his system, the fifth became the foundation
of the world.

Platonic Love is based on particular aspects of geometrical correspondence
between the first two of the five solids, which I discovered by
performing a simple mathematical equation: I counted the number
of edges in a tetrahedron and in a cube. I found that a tetrahedron
has exactly half as many edges as a cube. I therefore established
the equation that 1 tetrahedron + 1 tetrahedron = 1 cube, as an
experimental geometrical formula.

In order to create a visual representation, I constructed a moving
model. The symmetrically positioned tetrahedra slowly unite into
a cube, then the cube splits into two tetrahedra again. The duration
of the restructuring between the two end stages is significantly
longer than the moment in which the solids appear as distinct forms.
This intermediate stage appears relatively unstructured, in that
it displays a character which is difficult to define. If the motion
were to be frozen in this intermediate stage, there would be little
to suggest that the jumble of edges had any connection with a regular
solid.

The tetrahedron and the cube are precisely defined solids, and therefore
represent timeless geometrical relationships. They are connected
by the temporality of the metamorphosis. The decreasing/increasing
confusion of the intermediate forms does not satisfy the topology
of regularity; their irregularity is, however, the result of a precisely
calculated motion. Extracted from the continuity of motion, they
might be regarded as half solids, or the embryonic forms of solids.
If one looks instead at the continuity of motion, the whole of the
metamorphosis may be regarded as a multi-directional, pulsating
body, with two timeless forms at its end stages.

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