The Magic Encyclopedia ™

The Latin Component Hypercube
{note: investigative article}
(by Aale de Winkel)

The Latin Component Hypercube came into the picture when studying pandiagonal squares of compound order, and is a generalisation of the latin component square which play a role in the studies of those squares

The Latin Component Hypercube
The latin component hypercubes are defined as hypercubes with digits lower to the orders prime factors

trivial all elements are 1

binary elements are 0 and 1 only

pan n-agonal all 1-agonals and (broken) n-agonals are summing toward the order.
current order 9 square expertise show that every add '0' onto the trival hypercube need
be compensated by a '2' on every 1-agonal, in order to compensate also on each n-agonal
these compensating '2' must also ly on a n-agonal connected with the added 0. This fact
forces some symmetry into the panmagic component hypercubes.

order 4 add on

0 -1 1 0
1 0 0 -1
-1 0 0 1
0 1 -1 0 order 4 add on (square version)
The order 4 add on can be pasted anywhere onto the trivial, the shown pattern is only one of
many as long as the pattern is symmetrically expanded the pandiagonallyty of the component
square is preserved, the pattern is added to the numbers already in the square, as long as
numbers don't go below 0 or beyond the considered prime, the addition of the pattern is
allowed, continuing adding this pattern many a component square is obtained.

The Latin Component Hypercube
The latin component hypercubes are defined as hypercubes with digits lower to the orders prime factors
trivial	all elements are 1
binary	elements are 0 and 1 only
pan n-agonal	all 1-agonals and (broken) n-agonals are summing toward the order.
pan n-agonal	current order 9 square expertise show that every add '0' onto the trival hypercube need be compensated by a '2' on every 1-agonal, in order to compensate also on each n-agonal these compensating '2' must also ly on a n-agonal connected with the added 0. This fact forces some symmetry into the panmagic component hypercubes.
order 4 add on 0 -1 1 0 1 0 0 -1 -1 0 0 1 0 1 -1 0	order 4 add on (square version)
order 4 add on 0 -1 1 0 1 0 0 -1 -1 0 0 1 0 1 -1 0	The order 4 add on can be pasted anywhere onto the trivial, the shown pattern is only one of many as long as the pattern is symmetrically expanded the pandiagonallyty of the component square is preserved, the pattern is added to the numbers already in the square, as long as numbers don't go below 0 or beyond the considered prime, the addition of the pattern is allowed, continuing adding this pattern many a component square is obtained.