Up down left right forward backwards, but whats diagnol?

[Yoshi]

i guess the title kinda answers my question, dont u think?

[Geosphere]

Its a vector, which is a combination of other "Orthagonal" directions.

[Aale de Winkel]

Just to note out, every orthogonal in n-dimensions (or monagonal, as I call them in the magic hypercube) is a position (n-point) with a vector (n-vector) with only 1 non-zero entry (which can be taken to be 1).
A diagonal is then a linear combination of 2 of the n-vectors.
A triagonal simular but of 3 of these vectors, generalising:

An r-agonal is a linear combination of r indepent monagonal direction vectors.

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>
.

[Yoshi]

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>

Im not sure i understand that.

[Aale de Winkel]

Checkout the discussion I had with alkaline about my notation, elsewhere on this forum.

[Yoshi]

I sure will

[Polyhedron Dude]

Here are the diagonal, triagonal, and tetragonal directions in tetraspace:

let N,S,E,W,M,G,U,D represent north, south, east, west, marp, garp, up, and down.

diagonals:
NE, NW, NM, NG, SE, SW, SM, SG, EM, EG, WM, WG - horizontal
NU, SU, WU, EU, MU, GU, ND, SD, WD, ED, MD, GD - non-horizontal

triagonals:
NEM, NEG, NWM, NWG, SEM, SEG, SWM, SWG - horizontal
NEU, NED, NWU, NWD, NMU, NMD, NGU, NGD, SEU, SED, SWU, SWD, SMU, SMD, SGU, SGD, EMU, EMD, EGU, EGD, WMU, WMD, WGU, WGD - non horizontal

tetragonals:
NEMU, NEMD, NEGU, NEGD, NWMU, NWMD, NWGU, NWGD, SEMU, SEMD, SEGU, SEGD, SWMU, SWMD, SWGU, SWGD

Polyhedron Dude