Predavatelj: Dan Archdeacon (The University of Vermont, USA)
Steinitz’s Theorem states that a graph is the 1-skeleton of a convex
polyhedron if and only if the graph is 3-connected and planar. The
polyhedron is called a geometric realization of the embedded graph.
Its faces are bounded by convex polygons whose points are coplanar.
polyhedron if and only if the graph is 3-connected and planar. The
polyhedron is called a geometric realization of the embedded graph.
Its faces are bounded by convex polygons whose points are coplanar.
What about graphs on the torus, specifically triangulations? Given a
triangulation that has the topological shape of a torus, can it be
realized in 3-space using only flat triangles? What about other surfaces?
What about non-triangulations?
In this talk we examine these issues using some surprising techniques
including a detour into the fourth dimension.
Joint work with Paul Bonnington, and Jo Ellis-Monaghan.
