The Quaternion Group as a Symmetry Group

TL;DR

This paper explores the quaternion group, a mathematical structure with eight elements, and proposes a method to realize it as the symmetry group of a physical sculpture, filling a gap in symmetry group applications.

Contribution

It introduces the quaternion group as a symmetry group for physical objects, providing a novel approach to representing this mathematical structure in tangible form.

Findings

Quaternion group formally described and intuitively explained

Strategy for constructing a sculpture with quaternion symmetry outlined

Potential applications in art and physics suggested

Abstract

We briefly review the distinction between abstract groups and symmetry groups of objects, and discuss the question of which groups have appeared as the symmetry groups of physical objects. To our knowledge, the quaternion group (a beautiful group with eight elements) has not appeared in this fashion. We describe the quaternion group, both formally and intuitively, and give our strategy for representing the quaternion group as the symmetry group of a physical sculpture.