Free constructions of geometries of Coxeter type

TL;DR

This paper introduces two new methods for constructing geometries of Coxeter type, expanding the toolkit for understanding these mathematical structures.

Contribution

It provides two free construction techniques for geometries of Coxeter type, applicable to specific classes of Coxeter diagrams.

Findings

Constructed geometries for diagrams without A_3 subdiagrams

Developed constructions for diagrams of types C_n and H_4

Enhanced understanding of Coxeter geometries

Abstract

We establish two free constructions of geometries of Coxeter type. The first construction deals with any Coxeter diagram having no subdiagram of type A_3, the second one with diagrams of type C_n and H_4.