## Construction of flexible polyhedra

**Goal:**
It has been known since Legendre and Cauchy that
convex polyhedra in Euclidean space are always rigid, that
is, they cannot be deformed without changing the ''shape''
or their faces. However, non-convex polyhedra can be
flexible, the first examples were discovered by R. Connelly
in 1968.
There are a number of known examples of flexible polyhedra.
The goal of the project will be to find explicit and exact
descriptions of some of those examples, that is, compute
the coordinate of the vertices as a function of the deformation
parameter.
A possible second stage of the project will be to check
whether some quantities are conserved in a deformation.
It is known that the volume of flexible polyhedra remains
constant, as well as other quantities like the total mean
curvature. However other quantities might be constant
in a flex.

**Schedule:** to be determined.

**Persons involved:**
Advised by Jean-Marc Schlenker, NN.

**Difficulty level:**
Introductory.

**Tools:**
programs in python/sage.

**Expected results:**
Construct explicitly some examples of flexible polyhedra.
Those examples might be used later in other EML projects.