Tiger Tiger. burning bright, In the forests of the night; What immortal hand or eye. Could frame thy fearful symmetry?The Tiger, by William Blake

Beside the actual universe I can set in imagination other universes in which the laws are different J. L. Synge

## Artworks on Complex Polytopes

Below are the results of my messing around with complex polytopes. I try to juxtapose a set of some philosophical statements (or bullshits) within a group of related complex multi-dimensional geometrical forms. Both, the words and the images of regular complex polytopes in unitary space, are saying the same philosophy. The arrangement of the simplest shape like lines is able to construct compositions that accentuate both the simplicity and the complexity of some concepts in life.

The artworks are created from the composition of a set of projections of complex polytopes into Euclidean space. A complex polytope p{q}r is a polygon in the unitary plane (whose coordinates are (z1,z2) where both are complex number) with p-edges (an edge with p-vertices) and each vertex belongs to r of the edges. The number q is the length of minimal cycle of the vertices such that every consecutive two belong to an edge [Coxeter and Shephard, in Visual Mind, 1993, p. 19]. Two of such polytopes are used here: Hessian polyhedron (in 3-dimensional unitary space or 6-dimensional real space) and Witting polytope (in 4-dimensional unitary space or 8-dimensional real space).

Each individual projection of a complex polytope is generated using Mathematica and is saved as an EPS file. The EPS files are imported to Adobe Illustrator using a script that also composes the arrangement of these objects. Words are then added manually.