Tetra-Lattices

From: PaulHjelmstad <phjelmstad@xxxxxxx>
Date: Wed, 29 Aug 2007 10:33:33 EDT

I would like some help with the Tetra-Lattices article
on Moonshine Math

http://www.neverendingbooks.org/

1. Please explain what a vector of norm 4 and norm 8 are

(Here he gives +-(3,-1,-1,-1) as norm 4 and +-(1,3,1,-1_
as norm 8, also +-(-3,-1,-1,-1) as norm 4 and +-(1,-3,1,-1) as norm 8

2. Don't see why the inproduct of (3,-1,-1,-1).(1,3,1,-1) = -1 and (-3,-1,-1,-1).(1,-3,1,-1) =2

3. The squared lengths of the vectors are 1/12, 7/12, 13/12 and 19/12, how are these obtained (dot product?) Obviously these are not even. Please see the link..

I'd post a question right on that blog, but I what to
get beyond elementary things first.
.

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