Császár polyhedron

The Császár polyhedron ( Hungarian: [ˈt͡ʃaːsaːr], 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. As an abstract polytope, it is regular.

It has 14 irregular triangular faces, 7 vertices, and 21 edges. 6 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.

It can be seen as a 3D topological equivalent of the 7-2 step prism, sharing its vertex and edge counts and also having no diagonals.