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%I #16 Jun 04 2022 14:15:27
%S 8,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,4,4,0,0,0,0,0,0,0,0,
%T 0,0,0,0,0,0,0,0,0,0,0,0,0,0,4,0,4,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
%U 0,0,0,0
%N A generator matrix for the Leech lattice, multiplied by sqrt(8), read by rows.
%C There are infinitely many such matrices, this just happens to be a concrete example that we gave in the Sphere-Packing book. It is not unique in any way. - _N. J. A. Sloane_, Jun 04 2022
%H Paolo Xausa, <a href="/A353294/b353294.txt">Table of n, a(n) for n = 1..576 (rows 1..24 of the matrix, flattened)</a>
%H J. H. Conway and N. J. A. Sloane, <a href="https://doi.org/10.1007/978-1-4757-6568-7">Sphere Packings, Lattices and Groups</a>, 3rd edition, Springer, New York, NY, 1999, pp. 131-133.
%H Wikipedia, <a href="https://en.wikipedia.org/wiki/Leech_lattice">Leech lattice</a>.
%H Wikipedia, <a href="https://en.wikipedia.org/wiki/Miracle_Octad_Generator">Miracle Octad Generator</a>.
%F det(A/sqrt(8)) = 1, where A is the present matrix.
%e As depicted by Conway and Sloane (1999), p. 133, the full 24 X 24 matrix is given below, in standard MOG (Miracle Octad Generator) coordinates.
%e .
%e 8 0 0 0 | 0 0 0 0 | 0 0 0 0 | 0 0 0 0 | 0 0 0 0 | 0 0 0 0
%e 4 4 0 0 | 0 0 0 0 | 0 0 0 0 | 0 0 0 0 | 0 0 0 0 | 0 0 0 0
%e 4 0 4 0 | 0 0 0 0 | 0 0 0 0 | 0 0 0 0 | 0 0 0 0 | 0 0 0 0
%e 4 0 0 4 | 0 0 0 0 | 0 0 0 0 | 0 0 0 0 | 0 0 0 0 | 0 0 0 0
%e --------|---------|---------|---------|---------|--------
%e 4 0 0 0 | 4 0 0 0 | 0 0 0 0 | 0 0 0 0 | 0 0 0 0 | 0 0 0 0
%e 4 0 0 0 | 0 4 0 0 | 0 0 0 0 | 0 0 0 0 | 0 0 0 0 | 0 0 0 0
%e 4 0 0 0 | 0 0 4 0 | 0 0 0 0 | 0 0 0 0 | 0 0 0 0 | 0 0 0 0
%e 2 2 2 2 | 2 2 2 2 | 0 0 0 0 | 0 0 0 0 | 0 0 0 0 | 0 0 0 0
%e --------|---------|---------|---------|---------|--------
%e 4 0 0 0 | 0 0 0 0 | 4 0 0 0 | 0 0 0 0 | 0 0 0 0 | 0 0 0 0
%e 4 0 0 0 | 0 0 0 0 | 0 4 0 0 | 0 0 0 0 | 0 0 0 0 | 0 0 0 0
%e 4 0 0 0 | 0 0 0 0 | 0 0 4 0 | 0 0 0 0 | 0 0 0 0 | 0 0 0 0
%e 2 2 2 2 | 0 0 0 0 | 2 2 2 2 | 0 0 0 0 | 0 0 0 0 | 0 0 0 0
%e --------|---------|---------|---------|---------|--------
%e 4 0 0 0 | 0 0 0 0 | 0 0 0 0 | 4 0 0 0 | 0 0 0 0 | 0 0 0 0
%e 2 2 0 0 | 2 2 0 0 | 2 2 0 0 | 2 2 0 0 | 0 0 0 0 | 0 0 0 0
%e 2 0 2 0 | 2 0 2 0 | 2 0 2 0 | 2 0 2 0 | 0 0 0 0 | 0 0 0 0
%e 2 0 0 2 | 2 0 0 2 | 2 0 0 2 | 2 0 0 2 | 0 0 0 0 | 0 0 0 0
%e --------|---------|---------|---------|---------|--------
%e 4 0 0 0 | 0 0 0 0 | 0 0 0 0 | 0 0 0 0 | 4 0 0 0 | 0 0 0 0
%e 2 0 2 0 | 2 0 0 2 | 2 2 0 0 | 0 0 0 0 | 2 2 0 0 | 0 0 0 0
%e 2 0 0 2 | 2 2 0 0 | 2 0 2 0 | 0 0 0 0 | 2 0 2 0 | 0 0 0 0
%e 2 2 0 0 | 2 0 2 0 | 2 0 0 2 | 0 0 0 0 | 2 0 0 2 | 0 0 0 0
%e --------|---------|---------|---------|---------|--------
%e 0 2 2 2 | 2 0 0 0 | 2 0 0 0 | 2 0 0 0 | 2 0 0 0 | 2 0 0 0
%e 0 0 0 0 | 0 0 0 0 | 2 2 0 0 | 2 2 0 0 | 2 2 0 0 | 2 2 0 0
%e 0 0 0 0 | 0 0 0 0 | 2 0 2 0 | 2 0 2 0 | 2 0 2 0 | 2 0 2 0
%e -3 1 1 1 | 1 1 1 1 | 1 1 1 1 | 1 1 1 1 | 1 1 1 1 | 1 1 1 1
%Y Cf. A008408, A260646, A351831.
%K sign,tabf,fini,full
%O 1,1
%A _Paolo Xausa_, Apr 12 2022