Q(rt6)
Disc=24
--------------------
n=4

Gram Matrix 
A=
[2,rt6+2,1,rt6+2]
[rt6+2,4*rt6+10,0,2*rt6+5]
[1,0,2,0]
[rt6+2,2*rt6+5,0,4*rt6+10]

h=4

Automorphism group sizes:
[1152, 128, 288, 288]

Neighbour Matrices:

N(P)=2

[0 9 0 0]
[1 0 4 4]
[0 9 0 0]
[0 9 0 0]

CharPoly = x^2(x-9)(x+9)

N(P)=3

[ 0  0 16  0]
[ 0 16  0  0]
[ 4  0  4  8]
[ 0  0  8  8]

CharPoly = (x-16)^2(x-4)(x+8)

N(P)=5

[ 0 36  0  0]
[ 4  0 16 16]
[ 0 36  0  0]
[ 0 36  0  0]

CharPoly = x^2(x-36)(x+36)

N(P)=49

[ 676    0  576 1248]
[   0 2500    0    0]
[ 144    0 1444  912]
[ 312    0  912 1276]

CharPoly = (x-2500)^2(x-700)(x-196)

--------------------
n=8

Gram Matrix
A oplus A

Mass = 22.32

Too big.