The Magic Encyclopedia ™

Models
(by Aale de Winkel)

Several modals for magic object are around for some time, this article shows some modals which are known to this author and the prescriptions he uses to formalize the modals.

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 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.

Template 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 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

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 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.
the donut model.	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 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.
Template	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	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