Modeling the hypercube.  

Mathematical models for the hypercube are quite common. here are just a few  
Modular Hyperspace 
In modular hyperspace an object is just repeated in every direction In this manner broken ragonals are unbroken because of repetition most commonly used for panmagic hypercubes, as such the panrelocation 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 2Points 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 circleline 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. 

Template 
A template for an order m hypercube is formed by a sequence of m^{n} hypercube positions or numbers [1..m^{n}] on positions within the hypercube it self. 

Modeling the hyperstar.  
Template 
Template are used by this author to depict the positions of numbers in a panmagic hypercube within a hyperstar, these hyprstars thus form panisomophic hyperstars Also of course templates can be formed by depicting permutation positions within a hyperstar 