PlanetPhysics/Animated Representation of 4D Space

4D-animated representation:

Ocneanu's Octacube Animation

Ocneanu's octacube animation and existing three-dimensional solid sculpture employed for the animation were described as follows.

Description of the `Octacube': "The subject of the projection is a regular 4-dimensional solid of intermediate complexity, which Ocneanu calls an ""octacube." It has 24 vertices, 96 edges and 96 triangular faces, which enclose 24 three-dimensional "rooms." Windows cut in faces allow the viewer to see within the structure, the same way that a window in a cubic room opens to the inside of the cube. Physically, the sculpture is a giant puzzle of 96 triangular pieces cut from stainless steel and bent into spherical shape; (a quote attributed to the octacube's inventor, Professor Adrian Ocneanu).

Note: The following is an example of a hand-drawn `mathematical diagram' by Alex Grothendieck around 1970 (perhaps a `dessin d'enfants' ? , or is it a 2D representation of an $n$-dimensional real space by Alex's `doodle' drawing ?)

*Click on the dessin d'enfants, blue text above, to link to the web site that has the downloadable images.