Editing Magic hypercube (section)

===Basic manipulations===
Besides more specific manipulations, the following are of more general nature
* '''^[perm(0..n-1)]''' : coördinate permutation (n == 2: transpose)
* '''_2<sup>axis</sup>[perm(0..m-1)]''' : monagonal permutation (axis ε [0..n-1])

Note: '^' and '_' are essential part of the notation and used as manipulation selectors.

====Coördinate permutation====
The exchange of coördinaat [<sub>'''k'''</sub>i] into [<sub>'''perm(k)'''</sub>i], because of n coördinates a permutation over these n directions is required. The term '''transpose''' (usually denoted by <sup>t</sup>) is used with two dimensional matrices, in general though perhaps "coördinaatpermutation" might be preferable.

====Monagonal permutation====
Defined as the change of [<sub>k</sub>'''i'''] into [<sub>k</sub>'''perm(i)'''] alongside the given "axial"-direction. Equal permutation along various axes with equal orders can be combined by adding the factors 2<sup>axis</sup>. Thus defining all kinds of r-agonal permutations for any r. Easy to see that all possibilities are given by the corresponding permutation of m numbers.

====normal position====
In case no restrictions are considered on the n-agonals a magic hyperbeam can be represented shown in '''"normal position"''' by:
:[<sub>k</sub>i] &lt; [<sub>k</sub>(i+1)] ; i = 0..m<sub>k</sub>-2 (by monagonal permutation)