# Renate Quehenberger, Quantum Cinema

"I was a somnambule guided by Plato’s world of ideas, dreaming of
Plato’s grandmother, drawing circles in the sand and now I am drawing
circles into silicon."

The pictures presented here were worked out in 3D animated geometry
during the Quantum Cinema project (funded by FWF) with a group of
scientists and digital artists. We were examining the geometrical
properties of 5-dimensional space and its significance in quantum
physics.

Currently I am pursuing my doctoral studies „On the Hermeneutics of
the Penrose Tilings".

My finding, the 3D representation of the Penrose kites and darts (P2),
the unit cell of 5-dimensional space, named "epitahedron" is exhibited
here in different configurations and media as prints and sculpture.

The Epita-dodecahedron is a composition of 12 polyhedra. Each of
the pentagonal faces is filled with one heptahedron, named
epitahedron.

It exhibits space filling properties in 4D space which can be
iterated ad infinitum - cf.Penrose Patterns - uniting dodecahedral
and icosahedral symmetries.

This picture is inspired by Henri Poincaré's description of the
homology sphere: instead of the pentagons, the epitahedra are
twisted against each other in counter-movements. It is the first
visual access to the resulting different evolving symmetries,
crystallizing in steps of 36 degrees, as foretold by Poincaré in
1904. Here the central lines of the edges are exposing the
Petersen graph which is used for the description of quantum
structures.

The dodecahedron can be created as a boundary shape of the faces
of two intersecting heptahedra, named epitahedra, in the framework
of an icosahedron. It is not mentioned by Plato, because it does
not fit into his concept of triangles and its discovery is
ascribed only to his student Theatetos, who first proved that
there are only five regular convex polyhedra, the platonic solids,
the shapes of the "four elements".

Plato added instead an obscure remark about the fifth element:
‘[…] since there is another fifth configuration, the god used it
for the ornamentation of the whole universe’. In fact epitahedra
are revealing one of his most beautiful triangles in projection
and can therefor be regarded as Plato's 5th element,

In the above epita-dodecahedron the 12 apices are intersecting
each other in a way that a four-dimensional analogue of the
dodecahedron arises, which contains naturally another dodecahedron
within a complex intersecting space configuration in the
center.

This picture shows the center with a complex intersecting space
configuration consisting of four different solids: another
dodecahedron and its dual the icosahedron, the icosidodecahedron
and a stellated icosidodecahedron.

This 4-dimensional dodecahedron unites the dodecahedral and
icosahedral symmetries and can be related to the 120-cell and the
600-cell (cf. drawing by Alicia Boole Scott around1900. This print
exposes the central forms in overlapping transparent layers.