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  "body": "\n## Summary\n\nA building is a [[simplicial complex|V8GZ0W1ZZ5]] glued together from copies of a Coxeter complex, called apartments, under strong compatibility rules.\nJacques Tits introduced buildings to give a geometric picture of reductive algebraic groups and of the [[groups of Lie type|NPEBABQ49M]].\nEach group with a BN-pair acts on a building, and the [[Bruhat decomposition|T91E86D0RH]] becomes a statement about the relative position of two chambers.\nBuildings of $p$-adic groups are spaces of nonpositive curvature, used much like symmetric spaces for real Lie groups.\n\n## Explanations\n\n### L1 human\n\nThink of a building as a large structure made of identical flat floors, the apartments.\nAny two rooms of the structure lie together on at least one floor.\nTwo floors that share two rooms can be laid on top of each other without moving those rooms.\nThe simplest infinite example is a [[tree|062D9KXJB1]] in which every vertex has at least three neighbours.\nIts apartments are the infinite straight lines through the tree.\n",
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