INDEX 159
rational
closure of PQFs, 35
normalized polyhedral cone, 73
periodic set, 46
ray
extreme , 132
open , 3
Recursive Decomposition Method, 139
reduction
algorithm, 17
domain, 17
theory, 2
Hermite , 17
Korkin-Zolotarev , 23
Minkowski , 19
Venkov , 17
Voronoi , 26, 35, 58
refinement, 57, 114
regulator, 57
relative volume, 77
repartitioning polytope, 69
representation
conversion, 132
of arithmetical minimum, 38
of periodic set, 37
representatives of arithmetical minimum, 3
restricted
automorphism, 134
isomorphism, 134
rigid
lattice, 113
quadratic form, 114
rigidity index, 72
rigorous MAXDET, 85
root lattice, 8, 31, 41, 45, 53, 75, 108, 112,
126, 127
Ryshkov
polyhedron, 27, 47
set, 38
Schl¨ afli polytope, 75, 126
secondary cone, 57, 60
cruiser, 59
of polyhedral complex, 75
of polyhedron, 74
contiguous , 67
T - , 67
T -generic , 67
secondary polytope, 57
semialgebraic set, 39
semidefinite programming bound, x
semidirect product, 47
separable, 96
shortest lattice vector, 5
Siegel modular variety, 66
simultaneous approximation, 24
smooth function, 39
space of invariant quadratic forms, 34
sphere covering, 10
density, 11
radius, 11
lattice , 11
thinnest , 11
sphere packing, 9
density, 7, 9
densest , 9
lattice , 6
spherical
2-design, 43, 126
t-design, 116
standard
lattice, 5
periodic set, 37
star, 57
strongly
eutactic, 43
perfect, 44
subdivision, 133
Delone , 57
polyhedral , 35
successive minimum, 21
supertope, 75
support cone, 31
Sylvester criterion, 3
symmetry group of quadratic form, 33
Taylor series, 39
T -equivalent
quadratic form, 50
secondary cone, 71
T -extreme Delone polytope, 129
T -flip, 68
thinnest (lattice) sphere covering, 11
topological Morse function, 128
totally real number field, 110
T -perfect form, 49
triangulation, 133
Delone , 57
T -rigidity index, 72
T -secondary cone, 67
unimodular
equivalent, 77
simplex, 75
totally , 79
unimodularity property, 24
unit ball, 5
universally optimal point set, x
upper facet, 69
Venkov reduction, 17
vertex of polytope, 132
vertex-set, 55
of polyhedron, 60
Voronoi
domain, 29, 40
graph, 30
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