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| Richter-Gebert J. — Realization Spaces of Polytopes, Vol. 164 |
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| Предметный указатель |
 -construction 5
2-sphere 4
3-connected 3 117
3-Polytope 3
3-polytopes 117
3-sphere 5 84
4-polytope 6
ab-manifold 154
Adapter 51
Adapter, generalized 149
Addition 6 10 41 59 113
Admissible basis 3
Admissible hyperplane 15
Admissible projective transformation 15 18 30
Affine basis 19 24
Affine configuration 15 33
Affine dimension 15
Affine equivalence 18
Affine functional 13
Affine hull 14
Affine transformation 13 18
Affinely independent 2
Algebra 1
Algebraic complexity 21
Algebraic geometry 2
Algebraic numbers 5 6 78 95
algorithmic complexity 77 78
Algorithmic Steinitz problem 77
Alternative construction 82 90 151
Altshuler, Amos 174
Andreev, E.M. 3 117
Arbitrarily prescribable 4—6 38 39 50 95
Associated cone 16
atomic 16
Balinski's theorem 117
Barnette, David W. 4 5 38 174
Basic building block 45
Basic building blocks 8
Basis 2
Basis of a diagram 88
Basis, admissible 3
Basis, Affine 19 24
Bokowski — Ewald — Kleinschmidt polytope 5 38 173
Bokowski, Juergen 5 38 173 174
Brueckner, Max 174
Building block, basic 45
Building block, composed 45
Cairns' smoothing theory 2 174
cell 120
Chirotope 112 163
Circle packing theorem 3 117
Cluster 100 103
Coatomic 16
Cocircuit 34 163
Cocircuit, external 34
Codimension 4
Combinatorial polytope 15 17 29
Combinatorial sphere 4
Combinatorial structure 16
Combinatorial type 1 16
Combinatorics 1
Complexity, algebraic 21
Complexity, algorithmic 77 78
Composed building block 45
Computation frame 42
Computation frame, normal 43
Computation frame, standardized 44
Computation, geometric 6
Cone 15
Cone, associated 16
Configuration, affine 15 33
Configuration, linear 15
conic 151
Connected sum 8 29
Connector 10 47
Construction diagram 45 58 61 63 66
Constructions 7 28
Contractible 4
Contraction 84
Convex hull 1 14
Convex polytope 15
Coordinates, homogeneous 15
Corollaries 6 95
Counterexamples 4
Covector 163
Crapo, Henry 133
Cross product 13
Cross ratio 43
cube 2 17 18 20 176
CYCLE 118
d-polytope 1 16
Defining equations 8 21
Dehomogenization 15
Deletion 84 118
Diagram 87 88
Differential topology 2
DIMENSION 1 4
Dimension of a cone 15
Dimension of a polytopal complex 87
Dimension of a polytope 15
Dimension, affine 15
Dimension, linear 15
Doubly exponential 6 81 95 175
Duality 24
Edge graph 3 120
Edge length, rational 176
Empty set 2
Equations, defining 21
Equations, polynomial 3 21
Equilibrium 123 133
Equivalence, affine 18
Equivalence, homotopy 3 5 6 23 95
Equivalence, Lawrence 36
Equivalence, linear 18
Equivalence, projective 18
Equivalence, rational 22 97
Equivalence, stable 5 22 71 97
Euclidean length 13
Euclidean scale 43
Eulers's Theorem 121
Ewald, Guenter 5 38 173
Existential Theory of the Reals 5 6 77 95
Exponential, doubly 6 81 95 175
Exponential, singly 4 140 175
External cocircuit 34
Extreme points 2
Face 1 16
Face lattice 1 16
Face lattice, polar 25
Facet 16
Fan 87 89
Fary, Istvan 119
Fibration, trivial 21
Finite lattice 2
Flag transitive 1
Flat, necessarily 8 31
Forbidden minors 6 84 95 151
Forgetful transmitter 10 48 81
Frame computation 42
Frame information 45
Functional, affine 13
Functional, linear 13
Gale diagram 5
Gale duality 4 5
Generalized adapter 149
Geometric computation 6
Geometry 1
Geometry, algebraic 2
Geometry, real discrete 2
Gluing 29
| Goodman, Jacob E. 81 175
Graph 3 117 118
Graph, planar 119
Graph, stress 122
Gruenbaum, Branko 4 13 174
Guenzel, Harald 2 97 101
Harmonic polytope 56
Harmonic set 55
Homogeneous coordinates 15
Homogenization 15
Homotopy equivalence 3 5 6 23 95
Homotopy type 21
Hopcroft, John E. 133
Hull, affine 14
Hull, convex 1 14
Hull, linear 14
Hull, positive 14
Hypercube 27
Hyperplane, admissible 15
Incidence structures 6
Inequalities, non-strict 21
Inequalities, polynomial 3 21
Information frame 45
Information line 113
Inner cell 88
Integral vertex coordinates 4
Interior edges 123
Interior vertices 123
k-face 16
Kahn, Peter J. 133
Kleinschmidt polytope 5 38
Kleinschmidt, Peter 4 5 38 173
Koebe, Paul 3 117
Labelings 14
Lattice, finite 2
Lawrence construction 34
Lawrence equivalence 36
Lawrence extension 7 32 33
Lawrence polytope 7 33
Lawrence, Jim 33
Length, euclidean 13
Lifting 117 133
Linear algebra 13
Linear configuration 15
Linear dimension 15
Linear equivalence 18
Linear functional 13
Linear hull 14
Linear transformation 13
Mani, Peter 4
Maxwell, James C. 133
McMullen, Peter 133
Menger's Theorem 121
Minors, forbidden 6 84 95 151
Mneev's, Universality Theorem 5 173
Mneev, Nicolai E. 5 97 173
Moduli spaces 2
Multiplication 6 10 41 62 113
Necessarily flat 8 31
Net 92
Non-polytopal sphere 5 84
Non-prescribable 5 6 38 39 50 95
Non-rational points 3
Non-rational polytope 5 6 78 95 174
Non-Steinitz Theorem 84 151
Non-strict inequalities 21
Nonlinear optimization 2
Normal computation frame 43
Normal form 41 68
NP-hard 5 6 77 95
Octagon 55 78
Onn, Shmuel 4 81
Optimization, nonlinear 2
Oriented matroid 5 7 32 112 163
Partially ordered set 16
Pascal's theorem 39
Path 118
Peripheral edges 123
Peripheral vertices 123
Perles, Micha A. 5 174
PL-sphere 17
Planar 3 117
Planar graph 119
Planet 165
Platonic solids 1
Point configuration 14 32
Points, extreme 2
Points, non-rational 3
Points, rational 4
Polar face lattice 25
Polar polytope 25
Polarity 24
Pollack, Richard 81 175
Polygon 42
Polynomial equations 3 21
Polynomial inequalities 3 21
Polytopal 16
Polytopal complex 87
Polytopal sphere 4
Polytopal tools 7
Polytope 1 15
Polytope for addition 59
Polytope for multiplication 62
Polytope, codimension four 5
Polytope, combinatorial 15 17 29
Polytope, convex 15
Polytope, four-dimensional 6
Polytope, harmonic 56
Polytope, high-dimensional 4
Polytope, non-rational 5 6 78 95 174
Polytope, polar 25
Polytope, switch 107
Polytope, three-dimensional 3 117
POSET 16
Positive hull 14
Prescribable 4—6 38 39 50 95
Primary semialgebraic set 3 8 21 41
prism 8 28 31 45
Problems 173
Product, cross 13
Product, scalar 13
Projection, stable 21 97
Projective equivalence 18
Projective plane 6
Projective scale 10 42 43 113
Projective space 93
Projective transformation 31
Projective transformation, admissible 15 18 30
Pyramid 8 28 31 45
Quadratic Cone 151
Quadrilateral ratio 100
Quadrilateral set 99 106
Ratio, cross 43
Ratio, quadrilateral 100
Rational edge length 176
Rational points 4
Rationed equivalence 22 97
Real discrete geometry 2
Realizability problem for 3-diagrams 95
Realizability problem for 4-polytopes 6
Realizability problem for codimension 4-polytopes 5
Realization 19
Realization space 1 3 20
Realization space of a 3-polytope 4 144
Realization space of a 4-polytope 6
Realization space of a codimension 4-polytope 5
Realization space of a connected sum 32
Realization space of a diagram 88
Realization space of a fan 89
Realization space of a Lawrence extension 36
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