|Modeling the hypercube.|
|Mathematical models for the hypercube are quite common. here are just a few|
In modular hyperspace an object is just repeated in every direction
In this manner broken r-agonals are unbroken because of repetition
most commonly used for panmagic hypercubes, as such the pan-relocation
becomes a mere translation in hyperspace
|the donut model.||The donut model is quite commonly used for depicting panmagic squares.|
Most common model for an order m square is to have m minor circles 2π/m apart
centered around a major circle. On the minor circles 2π/m apart the circles
are joined by circles parallel to the majaor circles, thus forming the 2-Points
of the square, when the donut is broken open.
A more elaborate modal is the three dimensional hypertorus
|the hypertorus model.||
The hypertorus model is quite commonly used for depicting panmagic squares.
the hypertorus can be seen as a generalisation of the donut model.
The hypertorus can be viewed upon as a series of circles running on top of
one another, in order to depict an order m hypercube each circle progresses
2π/m on top of the circle it is running on when the circle completes 2π
Thus continuing the hypertorus forms a single circle-line figure, upon which
a permutation of the intended numbers can be superimposed to complete the
model of the hypercube. The combined hypertorus model and mentioned number
permutation thus form a modal for the hypercube one dimension lower then
the dimension of the hypertorus itself.
A template for an order m hypercube is formed by a sequence of mn hypercube positions
or numbers [1..mn] on positions within the hypercube it self.
|Modeling the hyperstar.|
Template are used by this author to depict the positions of numbers in a panmagic hypercube
within a hyperstar, these hyprstars thus form pan-isomophic hyperstars
Also of course templates can be formed by depicting permutation positions within a hyperstar