examples:
x-axis [0,...,0] <1,0,.....0>
y-axis [0,...,0] <0,1,0,...0>
...
order m squares main diagonal [0,0] <1,1>
order m squares sub diagonal [0,m-1] <1,-1>
order m cubes main triagonal [0,0,0] <1,1,1>
order m cubes sub triagonal [0,m-1,0] <1,-1,1>
order m cubes sub triagonal [0,0,m-1] <1,1,-1>
order m cubes sub triagonal [0,m-1,m-1] <1,-1,-1>
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