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