Re: Cubic lattice or A3 lattice ? (CORRECTION)

Yupps! I forgot the factor 2 in two places:

126 cells in 7D
6-1-cells amount = 2 C(1,7) = 14
5-2-cells amount = 2 C(2,7) = 42
4-3-cells amount = 2 C(3,7) = 70
254 cells in 8D
7-1-cells amount = 2 C(1,8) = 16
6-2-cells amount = 2 C(2,8) = 56
5-3-cells amount = 2 C(3,8) = 112
4-4-cells amount = C(4,8) = 70

I wrote:
Inversely, the sequence of polytopes I named chordo-polytopes, which are pure mathematical
objects derived from the An lattices, are simply the sequence of chordoids generated by the
standard basis (as chords) of the Euclidean spaces. So, the chordoid theory I developed few
years ago, specifically for the musical needs, appears now a much more fundamental object.
I forgot to mention but without the zero vector, which is the center or these chordo-polytopes.

For instance, with the standard basis e1=(1,0,0,0), e2=(0,1,0,0), e3=(0,0,1,0), e4=(0,0,0,1) the chord
e1:e2:e3:e4 generates the chordoid
( 0,0,0,0) (-1,1,0,0) (-1,0,1,0) (-1,0,0,1)
(1,-1,0,0) ( 0,0,0,0) (0,-1,1,0) (0,-1,0,1)
(1,0,-1,0) (0,1,-1,0) ( 0,0,0,0) (0,0,-1,1)
(1,0,0,-1) (0,1,0,-1) (0,0,1,-1) ( 0,0,0,0)
containing the zero vector (0,0,0,0) and all the minimal vectors (norm = 2) in the lattice A3 which are the
vectors (w,x,y,z) where w,x,y,z are integers and w+x+y+z = 0.

Pierre