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    Geometry: Incidence geometry

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    1. Construct a model of incidence geometry that has neither the elliptic hyperbolic nor Euclidean parallel properties.
    2. Consider a finite geometry where the points are interpreted to be the six vertices of a regular octedron and the lines are sets of exactly two points.

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    Solution Preview

    1. We will construct a model of incidence geometry that has different parallelism properties for different choices of a line l and a point P on l. We will take 5 points.
    Firstly, every pair of points needs to have a line through them, and every line has to have at least two points on it. Also, we cannot have all the points on the ...

    Solution Summary

    Problems of Incidence Geometry