On Flexible Prismatic Polyhedra

TL;DR

This paper explores four types of flexible prismatic polyhedra derived from Bricard octahedra, highlighting their properties such as genus, dihedral angles, self-intersecting faces, and vertex motion as a single-variable function.

Contribution

It introduces four new classes of flexible prismatic polyhedra with specific geometric and topological properties, expanding the understanding of flexible polyhedral structures.

Findings

Four types of flexible prismatic polyhedra identified

Polyhedra exhibit non-constant dihedral angles during flexion

Vertex motion can be described as a function of a single variable

Abstract

We demonstrate the existence of four types of flexible prismatic polyhedra that can be derived or inferred from a consideration of Bricard octahedra and generalizations of Bricard octahedra. These flexible polyhedra are of genus 0 and 1, have dihedral angles all of which are non-constant under flexion, have faces that exhibit self-intersections, have an indefinite number of faces and have vertex motion that can treated as a function of a single variable.