Aspects
A hypercube knows n! 2n Aspectial variants, which are obtained by coordinate reflection ( --> ) and coordinate permutations ( --> i]) effectively giving the Aspectial variant:
nHm~R perm(0..n-1); R = k=0∑n-1 ((reflect(k)) ? 2k : 0) ; perm(0..n-1) a permutation of 0..n-1Where reflect(k) true iff coordinate k is being reflected, only then 2k is added to R. As is easy to see, only n coordinates can be reflected explaining 2n, the n! permutation of n coordinates explains the other factor to the total amount of "Aspectial variants"!
Aspectial variants are generally seen as being equal. Thus any hypercube can be represented shown in "normal position" by:
= min (by reflection) < ; k = 0..n-2 (by coordinate permutation)(explicitly stated here: the minimum of all corner points. The axial neighbour sequentially based on axial number)
Read more about this topic: Magic Hypercube
Famous quotes containing the word aspects:
“An atheist may be simply one whose faith and love are concentrated on the impersonal aspects of God.”
—Simone Weil (1909–1943)
“I suppose an entire cabinet of shells would be an expression of the whole human mind; a Flora of the whole globe would be so likewise, or a history of beasts; or a painting of all the aspects of the clouds. Everything is significant.”
—Ralph Waldo Emerson (1803–1882)
“The happiest two-job marriages I saw during my research were ones in which men and women shared the housework and parenting. What couples called good communication often meant that they were good at saying thanks to one another for small aspects of taking care of the family. Making it to the school play, helping a child read, cooking dinner in good spirit, remembering the grocery list,... these were silver and gold of the marital exchange.”
—Arlie Hochschild (20th century)