An infinitesimally nonrigid polyhedron with nonstationary volume in the Lobachevsky 3-space

TL;DR

This paper presents an example of a flexible polyhedron in Lobachevsky 3-space that can change volume during an infinitesimal flex, challenging assumptions about rigidity and volume invariance.

Contribution

It introduces the first known example of an infinitesimally nonrigid polyhedron with nonstationary volume in hyperbolic space.

Findings

Existence of an infinitesimally nonrigid polyhedron in Lobachevsky 3-space.

Construction of an infinitesimal flex that alters volume.

Volume is not stationary under the flex.

Abstract

We give an example of an infinitesimally nonrigid polyhedron in the Lobachevsky 3-space and construct an infinitesimal flex of that polyhedron such that the volume of the polyhedron isn't stationary under the flex.