## Applied Geometry and Discrete Mathematics: The Victor Klee FestschriftThis volume, published jointly with the Association for Computing Machinery, comprises a collection of research articles celebrating the occasion of Victor Klee's 65th birthday in September 1990. During his long career, Klee has made contributions to a wide variety of areas, such as discrete and computational geometry, convexity, combinatorics, graph theory, functional analysis, mathematical programming and optimization, and theoretical computer science. In addition, Klee made important contributions to mathematics, education, mathematical methods in economics and the decision sciences, applications of discrete mathematics in the biological and social sciences, and the transfer of knowledge from applied mathematics to industry. In honour of Klee's achievements, this volume presents more than 40 papers on topics related to Klee's research. While the majority of the papers are research articles, a number of survey articles are also included. Mirroring the breadth of Klee's mathematical contributions, this book shows how different branches of mathematics interact. It is a fitting tribute to one of the leading figures in discrete mathematics. |

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### Contents

Selfduality Groups and Ranks of Selfdualities | 11 |

Do Projections Go to Infinity? | 51 |

The Minimal Projective Plane Polyhedral Maps | 63 |

Packing Euclidean Space with Congruent Cylinders | 71 |

Extended EulerPoincare Relations for Cell Complexes | 81 |

Computing the Convex Hull in the Euclidean Plane | 91 |

Measures of FStars in Finitely Starlike Sets | 109 |

On SignNonsingular Matrices and the Conversion | 117 |

Volume Approximation of Convex Bodies by Circumscribed Polytopes | 309 |

Points Sets with Small Integral Distances | 319 |

Convex Minimizers of Variational Problems | 325 |

Flattening a Rooted Tree | 335 |

Every Tree is Graceful But Some are More Graceful than Others | 355 |

Centers and Invariant Points of Convex Bodies | 367 |

The Diameter of Graphs of Convex Polytopes and Vector Theory | 387 |

Multiply Perspective Simplices Desmic Triads | 413 |

Recognizing Properties of Periodic Graphs | 135 |

Some Regular Maps and Their Polyhedral Realizations | 157 |

Volumes of a Random Polytope in a Convex | 175 |

Bodies of Constant Width in Riemannian Manifolds | 181 |

Uniquely Remotal Hulls | 193 |

The Symmetries of the Cut Polytope and of Some Relatives | 205 |

Complete Descriptions of Small Multicut Polytopes | 221 |

A Hyperplane Incidence Problem with Applications | 253 |

Gaps in Difference Sets and the Graph of Nearly Equal Distances | 265 |

Remarks on 5Neighbor Packings and Coverings with Circles | 275 |

Symmetric Solutions to Isoperimetric Problems for Polytopes | 289 |

A Global Newton Method | 301 |

Submanifolds of the Cube | 423 |

Finite Unions of Closed Subgroups of the Dimensional Torus | 433 |

Regular Triangulations of Convex Polytopes | 443 |

On the Number of Antipodal or Strictly Antipodal Pairs | 457 |

MultiOrder Convexity | 471 |

Almost Orthogonal Lines in | 489 |

Exact Upper Bounds for the Number of Faces in dDimensional | 517 |

Stretchability of Pseudolines is NPHard | 531 |

A Zonotope Associated with Graphical Degree Sequences | 555 |

The Combinatorics of Bivariate Splines | 587 |

### Common terms and phrases

1980 Mathematics Subject 1991 American Mathematical 1991 THE VICTOR algorithm assume automorphism circles column combinatorial complex configuration congruent conjecture consider contains convex bodies convex hull convex sets corresponding CW complexes defines a facet denote density diagonal digraph dimension Discrete Mathematics Discrete Mathematics Volume distance edge ellipsoids equivalent Euclidean Euclidean space exists face facet-defining follows function geometry H. S. M. Coxeter Hence hyperplanes implies inequality integer intersection isometry isomorphic lattice Lemma linear Math Mathematics Subject Classification maximal convertible minimal multicut polytopes nodes obtained packing pairs periodic graph permutations plane points polyhedra polyhedral map polyhedron poset problem projection proof of Theorem Proposition prove rank regular satisfies Schlegel diagram Science and Discrete segment self-dual polyhedron self-dual tiling self-duality group sequence simplicial simplicial complex space sphere subset symmetry group triangle upper bound vector vertex vertices VICTOR KLEE VICTOR KLEE FESTSCHRIFT