# Geometry

From Groupprops

This term is related to: incidence geometry

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Template:Incidence system property

## Contents

## Definition

### Definition with symbols

An incidence system is termed a **geometry** if it satisfies the following additional conditions:

- Every maximal flag contains exactly one element of each type, viz every maximal flag has corank 0
- For any two distinct types, the bipartite graph on the union of elements of those types given by the incidence relation, is a connected graph

### Graph-theoretic definition

An incidence system is termed a **geometry** if the corresponding graph has the following properties:

- Every maximal clique in it has one vertex from each part
- The subgraph induced on any two parts is connected.