156 INDEX
convex
body, 7
cone, 3
hull, 28
polyhedron, 131
polytope, 132
covering
conjecture, 129
maximum, 122
optimizer, 90
pessimum, 83, 126
radius, 11
locally optimal lattice , 84
covering density, 11
of Delone polytope, 123
Coxeter lattice, 12, 77, 108
Coxeter-Todd lattice, 45
critical value
Hermite , 24
Minkowski , 25
cross polytope, 28, 127
C-type, 75, 100
Davenport’s conjecture, 22
dead-end, 67
decomposition
Cholesky , 5
double coset , 136
Iwasawa , 4
Delone polyhedron, 56
Delone polytope, 55
of quadratic form, 55
adjacent , 57
extreme , 75
GLd(Z)-equivalent , 57, 87
GLt
d
(Z)-equivalent , 57, 89
perfect , 75
T -extreme , 129
translational equivalent , 57
Delone subdivision, 57
Delone triangulation, 57
automorphism group of , 92
densest
m-periodic sphere packing, 38
lattice sphere packing, 8
sphere packing, 9
determinant
maximization problem, 85
of lattice, 6
surface, 29, 35
diamond property, 133
Diophantine
approximation, 23
equation, 1
best approximation, 23
simultaneous approximation, 24
distance of PQF, 86
domain
C-type , 75
fundamental , 17
L-type , 57
reduction , 17
Voronoi , 29
double coset, 136
dual
description problem, 132
polyhedral cone, 132
duality gap, 85
Eisenstein
form, 52
integer, 52
lattice, 49
perfect form, 52
ellipsoid, 3
E-perfect form, 52
equivalent
arithmetically , 2
G-∼ , 50
(G, t)-∼ , 50
T -∼ , 50, 71
translational , 57
(T, t)-∼ , 50, 71
unimodular , 77
Euclidean
minimum, 111
norm, 5
norm best approximation, 25
number field, 111
unit ball, 5
eutactic
quadratic form, 34
strongly , 43
extremal lattice, 34
extreme
Delone polytope, 75
lattice, 34
quadratic form, 34
ray, 132
m-∼ , 39
periodic , 43
face, 132
lattice, 132
adjacent , 132
face-to-face, 36
facet, 131
lateral , 69
lower , 69
upper , 69
Fincke and Pohst algorithm, 31
fluid diamond packing, 41
fundamental domain, 17
Gaussian
form, 53
integer, 53
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