On the flexibility of Siamese dipyramids

TL;DR

This paper explores the apparent contradiction between the known mathematical rigidity of Siamese dipyramids and their observed physical flexibility, providing a mathematical explanation for their flexible behavior.

Contribution

It introduces a simple mathematical method to explain the physical flexibility of Siamese dipyramids despite their mathematical rigidity.

Findings

Physical models of Siamese dipyramids exhibit flexibility.

A mathematical method explains the discrepancy between model behavior and mathematical rigidity.

The study clarifies the conditions under which these polyhedra are flexible.

Abstract

Polyhedra called Siamese dipyramids are known to be non-flexible, however their physical models behave like physical models of flexible polyhedra. We discuss a simple mathematical method for explaining the model flexibility of the Siamese dipyramids.