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  "body": "\n## Summary\n\nA Buekenhout geometry, or diagram geometry, is a set of objects of several types with a symmetric incidence relation.\nEvery flag of pairwise incident objects extends to a chamber, which contains one object of each type.\nIt generalizes [[projective spaces|ZT9A6JK8QF]], [[generalized polygons|PCT2HY9AAZ]] and Tits buildings.\nFrancis Buekenhout introduced a diagram that records, for each pair of types, which rank $2$ geometries appear.\nThese diagrams are used to describe and classify geometries, including geometries for sporadic simple groups.\n\n## Explanations\n\n### L1 human\n\nA projective space has points, lines, planes and so on, and a point lies on a line, a line lies in a plane, and so forth.\nA Buekenhout geometry keeps only this pattern: objects of different types and a relation saying when two objects are incident.\nEach pair of types gives a small two-type geometry, such as a projective plane or a generalized quadrangle.\nA diagram with one node per type and labelled edges records these pairs, much like a Dynkin diagram.\n",
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