click to view the MPEG movie (cliquez pour voir le film MPEG)

Rotation about the X axis of the 32 vertices of a 5-cube [Rotation autour de l'axe X des 32 sommets d'un hyper-cube à 5 dimensions].




Let E be a N-dimensional space. It contains a set S of points {P(i)} with coordinates {C(1),C(2),...,C(N)}. The set S is visualized using a tridimensional euclidian space {OX,OY,OZ}:

Next figure displays a tridimensional (N=3) point (with coordinates {C(1),C(2),C(3)}) as a triangle:


                         X(3) +                                       + X(2)
                                +                                   +
                                  +                               +
                                    +                           # C(2)
                                      +                       + */*
                                        +                   +   *///*
                                          +               +     */////*
                                            +           +       *///////*
                                              +       +         */////////*
                                                +   +           *///////////
                    - - - - - - - - - - - - - - - O + + + + + + +/+/+/+/+/+/# + + X(1)
                                                -   -           */////////C(1)
                                              -       -         */////////*
                                            -           -       *///////*
                                          -               -     */////*
                                        -                   -   *///*
                                      -                       - */*
                                    -                           # C(3)
                                  -                               -
                                -                                   -
                              -                                       -
assuming that:

                    C(1) > 0
                    C(2) > 0
                    C(3) < 0



See miscellaneous set of points:




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