Corpus Hypercubus

Crucifixion (Corpus Hypercubus)

Salvador Dalí (1954)

Salvador Dalí, the master of surrealism, had a keen interest in natural science and mathematics. He was fascinated by hypercube, and it is featured in the painting Crucifixion (Corpus Hypercubus). Here Christ is crucified on figure of unfolded hypercube.

Hypercube is four-dimensional analogy of three-dimensional cube. It comes in by shifting three-dimensional cube perpendicular to three axis of our space. It consists of eight cubes. Frequently it depicted in it's frontal view as you can see in the image right. As cube can be unfolded into flat figure of six squares, hypercube can be unfolded into three-dimensional construction of eight cubes. This construction we see at Dalí's artworks, in particular.

Jenn 3D

Images above and on the right were created using computer program Jenn 3D which can draw graphs of finite Coxeter groups on four generators. Jenn builds the graphs using the Todd-Coxeter algorithm, embeds them into the 3-sphere, and stereographically projects them onto euclidean 3-space. The models really live in the hypersphere so they looked curved in our flat space.

Jenn 3D is licenced under version 2 of GNU public license. You can download executable file from developer's site. Unfortunately, developer does not provide executable for Windows platform at present, but he says you can download the source and compile it yourself.