Geometric Hyperplanes: Desargues Encodes Doily
Metod Saniga
TL;DR
This paper demonstrates that the structure of the generalized quadrangle of order two can be fully represented using the properties of the Desargues configuration, linking geometric hyperplanes to quadrangle points and lines.
Contribution
It introduces a novel encoding of the generalized quadrangle of order two through the geometric hyperplanes of the Desargues configuration.
Findings
The structure of the quadrangle is fully encoded in Desargues configuration hyperplanes.
Points correspond to hyperplanes, lines correspond to specific triples of hyperplanes.
A new geometric representation linking two classical configurations.
Abstract
It is shown that the structure of the generalized quadrangle of order two is fully encoded in the properties of the Desargues configuration. A point of the quadrangle is represented by a geometric hyperplane of the Desargues configuration and its line by a set of three hyperplanes such that one of them is the complement of the symmetric difference of the remaining two and they all share a pair of non-collinear points.
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Taxonomy
TopicsComputational Geometry and Mesh Generation · Geographic Information Systems Studies