# Terms

## New Terms

Some terms used on this site:

the cells of each complement pair touch at a cell corner
the cells of each complement pair touch at a cell side
back diagonal, forward diagonal
back diagonal:      main diagonal with top to the left, (leans back)
forward diagonal: main diagonal with top to the right, (leans forward)
by analogy with backslash \ and forward slash /
borders
the border of the square and the border of each concentric subsquare
border paired
each border consists of complement pairs
octant boundaries
for odd order:  the middle row, middle column, and main diagonals
for even order: the two middle rows, two middle columns, and main diagonals
middle symmetric
of octant boundaries: symmetrical about the middle, (see Notes)
octant
any of the 8 divisions of the square between the octant boundaries, not including the boundaries
octant paired
border numbers in all the octants combined are complement pairs
symborder
octant paired with middle symmetric octant boundaries

square side
top or bottom side of the square not including the middle row(s), or
left or right side of the square not including the middle column(s)
opposite paired
octant paired with the complement pairs on opposite square sides
side paired
octant paired with the complement pairs on the same square side
symmetric side paired
side paired with the complement pairs symmetric about the center of the row or column
symlateral
symmetric side paired with middle symmetric octant boundaries,
(for even order, these can be only near-symlateral, see Even Note)
hybrid
having side to side characteristics of two square types, for example:

Odd Note:
For odd order square boundaries, this is the same as center symmetric.

Even Note:
For even order squares, in the 2x2 center not all rows, columns, and main diagonals can be middle symmetric. For the ones that are not, the containing boundary must contain another pair of cells that are not complementary. This is required so that the total of the four cells is the sum of two complementary pairs.
So, for all even order squares, up to eight pairs have be placed non-symmetrically for some boundary.

If you know of other terms for these features or different uses of these terms, please send an email to sharrywhite@budshaw.ca.