Generating Combinatorial Complexes of Polyhedral Type
Egon Schulte · Transactions of the American Mathematical Society · 1988
The paper describes a method for generating combinatorial complexes of polyhedral type. Building blocks ${\mathbf {B}}$ are implanted into the maximal simplices of a simplicial complex ${\mathbf {C}}$, on which a group operates as a combinatorial reflection group. Of particular interest is the case where ${\mathbf {B}}$ is a polyhedral block and ${\mathbf {C}}$ the barycentric subdivision of a regular incidence-polytope ${\mathbf {K}}$ together with the action of the automorphism group of ${\mathbf {K}}$.