Christopher J. Kimmer, Ph.D.
IU Southeast Informatics
iSci
the informatics of scientific computing
The Voronoi Construction at t = 1
The dual structure to a Voronoi cell complex is known as the Deloné
triangulation (in 6D the ``triangles'' are six-dimensional simplices),
and the structure of both entities can be calculated for the extrema
of
Ψ
(
x
)
at
t
= 1
,
the 6D BCC lattice. The Deloné edges dual to these Voronoi faces are quite
simple with respect to the 6D hyperoctahedral group. For instance, about the
origin the Deloné edges connect the origin to points like
{100000}
or
to the 64 points made up of
½
. The faces corresponding to
{100000}
are eliminated, and all the others are kept. This cell complex
agrees with the sign of
Ψ
(
x
)
(at
t
= 1
)
over 96% of 6-space based on a Monte Carlo
sampling of points; planar cuts of this 6D structure are shown in
Figure
2.10
.
Chris Kimmer 2011-06-01