## Finite Geometries |

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### Contents

Embedding Finite Planar Spaces in Projective Spaces | 9 |

Locally Polyhedral Graphs 2 3 | 23 |

Harmonic Ovals of Even Order | 65 |

Copyright | |

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### Common terms and phrases

2-connected affine plane algebraic apartment system assume automorphism group autotopism B-oval Bezout domain blocking set collinear collineation group complex construction contains Corollary Coxeter defined denote Desarguesian Desarguesian plane diagram elements equation example exists Finite Geometries fixes flag-transitive framework GF(q 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 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 points polytopes prime power projective plane projective space Proof Proposition proved quadrangles quadric regular result satisfies secant secant line simply connected Steiner system subgroup subset subspace Suppose tactical decomposition Tallini tangent line Theorem transitive translation plane transvection unique vertex vertices