Császár polyhedron

The Császár polyhedron (approximate English pronunciation CHA-sar) is a toroidal polyhedron without any diagonals; that is, every pair of vertices is connected by an edge. It is the dual of the Szilassi polyhedron.

It has 14 irregular triangular faces, 7 vertices, and 21 edges. 7 faces meet at each vertex.

Its vertices and edges can be seen as an embedding of the complete graph K7 onto a torus of genus 1.