The Magic Encyclopedia ™

The Latin Hypercube
(by Aale de Winkel)

The Latin Hypercube is a Hypercube consitsting of only digits, in most cases these digits can be changed by a digit changing permutation. Because of this any latin hypercube with main n-agonal with equal digits can be "digitally changed" into a "zero n-agonal". Main n-agonal permutation can be used to order a main n-agonal, thus giving an ordered latin hypercube.

The Latin Hypercube
The latin hypercubes form the components of the hypercube, below the several types
of latin hypercubes are defined (definitions might be taken from the lexicon)

pure all 1-agonals and all n-agonals contain all m digits

regular all 1-agonals contain all m digits, all n-agonals need not contain all digits
but do sum up to the magic sum.

bare all 1-agonals contain all m digits

zero n-agonal a bare latin hypercube with the main n-agonal all '0'
relevant subject Hypercube doubling method

ordered a pure latin hypercube with the main n-agonal in natural ordering
relevant subject MultiMagic hypercube

normalized the axes 1-agonals contain higher permutations with increasing axis number.
in case of equal 1-agonal axes, the need to transpose might follow from
following 1-agonals parrallel to the given axis.

The Latin Hypercube
The latin hypercubes form the components of the hypercube, below the several types of latin hypercubes are defined (definitions might be taken from the lexicon)
pure	all 1-agonals and all n-agonals contain all m digits
regular	all 1-agonals contain all m digits, all n-agonals need not contain all digits but do sum up to the magic sum.
bare	all 1-agonals contain all m digits
zero n-agonal	a bare latin hypercube with the main n-agonal all '0'
zero n-agonal	relevant subject	Hypercube doubling method
ordered	a pure latin hypercube with the main n-agonal in natural ordering
ordered	relevant subject	MultiMagic hypercube
normalized	the axes 1-agonals contain higher permutations with increasing axis number. in case of equal 1-agonal axes, the need to transpose might follow from following 1-agonals parrallel to the given axis.