## Finite Geometries |

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### Contents

Sets of Type 1 k k + 1 in Projective Planes | 2 |

The Locally Icosahedral Graphs | 19 |

Harmonic Ovals of Even Order | 65 |

Exterior Sets with Respect to the Hyperbolic | 83 |

Linear Spaces and Groups 10 3 | 103 |

Spreads Obtained from Ovoidal Fibrations | 117 |

A Class of Rank 32Planes | 131 |

Translation Planes of Order n Which Admit | 149 |

A Search for a NonDesarguesian Plane of Prime Order | 199 |

Some Remarks on Covers and Apartments | 223 |

Hyperovals and Generalized Quadrangles | 251 |

A Characterization of the Set of Lines Either | 271 |

Extensions of Regular Complexes | 289 |

On Sets of Given Type in a Steiner System | 307 |

The kSets of PGrq from the Character Point of View | 321 |

The Projective Geometry of Rigid Frameworks | 353 |

### Common terms and phrases

1-factors 2-connected affine plane apartment system assume automorphism group autotopism B-oval blocking set c-set collinear collineation group complex construction contains Corollary Coxeter defined denote Desarguesian Desarguesian plane diagram elements example exists Finite Geometries finite projective fixes flag-transitive Foulser framework GF(q given GQ of order graph group of order harmonic oval Hence implies incidence structure infinitesimal motion integer intersection inversive plane involutions isomorphic k-set Kantor Laguerre plane latin squares Lemma Let G Let Q linear space lines of type Math maximal exterior set non-trivial orbits order q orthogonal maps ovoid pairs partition permutation permutation group planar space plane of order polytopes prime power projective plane Proof Proposition proved quadrangle quadric regular resp result satisfies secant line simply connected spreads Steiner system subgroup subset subspace Suppose tactical decomposition Tallini tangent line Theorem transitive translation plane transvection unique vector vertex vertices

### Popular passages

Page 373 - L. Lovasz, and Y. Yemini, On generic rigidity in the plane. SIAM J. Alg. Disc. Meth., 3, 91-98, 1982.