E_8: atlas

[Vavilov Nikolai]

 

Dear All, that's the paper that contains a graphical description of E_8, the 120

balls in the 8-dimensional Euclidean space, touching the central ball of the

same size on the positive side --- there are further 120 balls opposite to them,

of course.

In Figure 24 the central ball is represented by the 8 right-most nodes, approached

by 8 other balls from the 8 fundamental directions, all other balls are somewhere in

between.

There are many further ways to depict E_8, but for me this one not being the most

symmetric one, is the most informative one, since it immediately tells you, how many

balls are touching TWO of those (the central and another one), THREE of those, etc.

With some practice, you can visualise the whole configuration in the 8-dimensional

space.

This is also my only paper that was published TWICE in ENGLISH (first, as a sample

of what they can typeset in volume 0 of Documenta Mathematica, then as a regular

paper in IJAC).

 

N.V.