The Hypercube, the second regular solid in a four dimensions space  - 1974

""... I do not think it possible to build a hypercube different from those described by famous geometricians such as Caxeter"

Such a statement by scientist G. Arcidiacono would have discouraged anyone.

But my creative innocence made it possible. The happier with the result was Arcidiacono himself, but I was delighted too ancd after this success, always experimenting with mirrors, gave form the   pentacell and sixteencells respectively the first and the third regular solid in a four dimensions space."



::..Un incontro con il "Divino Cubo"..::

"In one dimension did a point in movement not generate a line with two terminal points? "In three dimensions did not a square in movement generate - and did not this eye of mine perhaps observe it - that blessed entity, a cube, with eight terminal points? "And in four dimensions will not a cube in movement give rise - alas for the Analogy and alas for the Progress of Truth if this were not so! - will it not give rise, I was saying, the movement of the divine cube, to a more divine Organism with sixteen terminal points? "And therefore does it not necessarily follow that the more divine offspring of the divine Cube in the Land of Four Dimensions will have to be delimited by eight Cubes: and is not this too, as my Lord has taught me to believe, in strict accordance with the analogy?"

The dialogue quoted above takes piace between the square, the protagonist of the book, and the here who comes to visit him. The book from which it is taken is "Flatland",that is to say the world of only two dimensions. The book was written by Edwin A. Abbott exactly one hundred years ago. This episode refers to the shattering made by the square, a flat figure of only two dimensions, thanks to the sphere, a creature inhabiting three-dimensional space like ourselves, who revealts to the square the existence of an ulterior dimension, or of at least one more.

We would be similary overwhelmed if we were to encounter by chance a creature of the fourth dimension.

But the fact is that I have had just such an adventure more than once. The first occasion was while watching on the terminal of an elaborator an animated film about the hypercube (the divine cube of the land of four dimensions) made by the mathematician Thomas Banchoff.

A second time it happened in a pine wood at EUR in Rome. Large metal objects were hanging from the trees, the regular solids of four-dimensional space. The large sculptures, for that is what the objects were, rotated in the air reflecting the surroundings expecially for the unsuspecting passers - by who didn't know what was happening. 

In reality the sight of thosefour-dimensional objects was anticipated - more than that, it was prepared with care, so much so that the whole scene was shot with a movie camera and anyone can see the account of these near encounters in the film "Dimensions" that I made in 1982.

The autor of this encounter was Attilio Pierelli. Like the square in "Flatland", who having seen the third dimension tried to convince his countrymen of its existence, Pierelli tried to make the land offour dimensione visible to those who had never been there.

The notable advantage that Pierelli had over the book was that the object he saw there he was able to bring back with him to our world and that we could touch them and be reflected in them thereby imagining to be on a voyage in the highest dimension".

< Michele Emmer >
estratto da "Le Parole Rampanti" 1985..::

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