Crucifixion

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CORPUS HYPERCUBUS by Salvador Dali.

Jesus crucified on a net of a hypercube, i.e. 4-dimensional cube. Mother Mary standing before the dual of the 4-dimensional crosspolytope, hovering above a checkerboard pattern. If you completely climb up the ladder of the A-D-E series and make the step E7 to E8, he does appear as "the octonion at infinity" or "the Observer in 3-dimensional space" or in terms of a physics model: the lab system or Newton's absolute space. The Observer 'sees' an empty space in which there are no things and so there is no body for the Observer. As soon as there would be, the observer enters a relative space and time.

THOUGHT EXPERIMENT:

The lowest cube of the net (the one behind the feet) has come loose from Golgotha (=Skull place). Move your thought from your skull to this cube (call this one the Skull cube).

His hands have come loose so they can turn around and glue the four cubes that are behind his arms, together (to do this the cubes have to be deformed, shaping them in a sort of rectangular torus).

His feet have come loose so glue the bottom square of the lowest cube to the top square of the upper cube (to do this the four cubes that are behind his head, body and legs must be deformed to form again a sort of rectangular torus: it is linked to the horizontal torus of four cubes).

The thorny crown on his head is gone: when the four horizontal cubes rotate along a vertical axis the four vertical cubes can rotate along with them.

The two sets of four cubes are already glued together by four squares so each set of four has 12 squares free after being glued to a rectangular torus. The four sides of the upper cube can be glued to the four upper squares of the horizontal torus. The four sides of the cube above the lowest can be glued to the four bottom squares of the horizontal torus. (A further deformation of the cubes is necessary). What about the last four squares of each torus?

The wound of his pierced heart is healed. The deformation of the lowest cube where your thought went to, has become really dramatic. Its four sides must be glued to the four outside squares of the horizontal torus. It has been completely turned inside out ! The cube behind his heart (let's call it the Heart cube) isn't hardly deformed. Now let's rotate the two linked rectangular torusses of four cubes simultaneously by 180 degrees (a half turn). The cube in which you think you are has changed place with the Heart cube. Now your thought is really in the heart of the universe where there is no centre or above or below or left or right or back or front. Taking up his cross it becomes light...

If all the squares are glued to another square in this way, four cubes come together at each vertex. The hypercube thus has 8 cubes, (8x8)/4=16 vertices and (8x6)/2=24 squares. At each edge there are 3 cubes and so there are (8x12)/3=32 edges. If we place a point in the centre of each cube and join the this centre to the 8 vertices of its cube, we achieve a beautiful regular figure with 16 + 8 = 24 vertices and 32 + (8x8) = 96 edges: the socalled 24-cell. Its cells are 24 regular octahedrons, based on the 24 squares of the hypercube.

The 8 centres that were added are the 8 vertices of the 4-dimensional analogue of the octahedron: the 4-dimensional crosspolytope. You can make a 3-dimensional projection as follows:

Start with the centre of the Heart cube (Heart centre). Place six vertices of an octahedron around this point. The centre of the Skull cube (Skull centre) is where you think you are watching the other seven vertices.