Skeletal Geometric Complexes and Their Symmetries

TL;DR

This paper explores skeletal polyhedral structures in three-dimensional space, focusing on those with maximal symmetry, and examines their geometric, combinatorial, and algebraic properties.

Contribution

It characterizes skeletal polyhedra and complexes with maximal symmetry, providing a comprehensive analysis of their geometric and algebraic features.

Findings

Classification of skeletal structures with maximal symmetry

Description of geometric and combinatorial properties

Analysis of algebraic symmetry groups

Abstract

Skeletal polyhedra and polygonal complexes are finite or infinite periodic structures in 3-space with interesting geometric, combinatorial, and algebraic properties. These structures can be viewed as finite or infinite periodic graphs (nets) equipped with a polyhedral superstructure imposed by the faces, allowed to be skew, zigzag, or helical. The article describes skeletal structures with maximal symmetry.