INDEX 157
lattice, 49
perfect form, 53
gift-wrapping step, 138
GLd(Z)-equivalent
t
Delone polytope, 57
quadratic form, 48
Gosset polytope, 75, 126
G-perfect form, 49
G-perfect form, 53
gradient, 35
graph
isomorphism problem, 136
traversal algorithm, 31
Hadamard’s inequality, 30
halfspace, 3, 28
Hermite
approximation, 24
critical value, 24
reduction, 17
’s constant, 6
’s continued fraction expansion, 25
Hessian, 43
hexagonal lattice, 6
homogeneous minimum, 3
surface, 98
homology, 37
Horvath lattice, 100
H-perfect form, 54
Hurwitz quaternionic
form, 53
integer, 54
lattice, 54
perfect form, 54
hypermetric cone, 75
hyperoctahedral group, 19
hyperplane, 28
Incidence Decomposition Method, 137
Recursive , 139
incidence number, 140
inhomogeneous minimum, 83
w.r.t. discrete set, 84
inner coefficient, 4
intersection property, 133
Iwasawa decomposition, 4
Jacobi identity, 4
Kepler’s conjecture, 9
kissing number, 7
Klein’s Modulfigur, 36
Korkin-Zolotarev reduction, 23
Kronecker product, 52
K-theory, 37
Lagarias
MCF expansion, 25
Lagrange expansion, 4
laminated lattice, 45
Las Vegas algorithm, 72
lateral facet, 69
lattice, 5
sphere packing, 6
Barnes-Wall , 54, 126
complex , 52
Coxeter , 12, 77, 108
Coxeter-Todd , 45
dual laminated , 12
Eisenstein , 49
extremal , 34
extreme , 34
Gaussian , 49
hexagonal , 6
Horvath , 100
Hurwitz quaternionic , 49
laminated , 45
Leech , 8, 45, 112
Minkowski reduced , 19
patchwork , 49
perfect , 30
reduced , 17
rigid , 113
root , 8, 31, 41, 45, 53, 108, 112, 126,
127
standard , 5
strongly eutactic , 43
strongly perfect , 44
well-rounded , 129
Leech lattice, 8, 45, 112
covering radius, 114
section of , 45
lifting map, 69
linear
automorphism group, 134
program, 34
programming bound, x
local lattice covering maximum, 122
locally
finite polyhedron, 28
optimal lattice covering, 84
optimal lattice packing-covering, 84
lower facet, 69
L-type domain, 57
MCF expansion, 24
additive , 25
Lagarias , 25
Minkowski geodesic , 25
measure zero set, 126
m-eutactic, 40
m-extreme, 39
isolated , 40
minimum
arithmetical , 3
Euclidean , 111
homogeneous , 3
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