A Curiosity Polyhedra

 A toroidal heptahedron. This is a very special polyhedron because it forms a ring or torus, that is, it has a hole that goes through it. It has 14 vertices and 21 edges. - Count the number of faces it has. -  Could you build a ring polyhedron of less faces? - Is it convex or concave? - Do the number of its faces, edges and vertices satisfy Euler's formula? What is the reason for this? - What does Eulerian polyhedron mean? Is this polyhedron Eulerian or non-Eulerian? - How many sides does each of its faces have? - Does each of its faces border all the other ones? - How many colours do you need to paint each face in a different colour, without two faces of the same colour touching each other? This shows the number of colours needed to paint a map that covers a ring-shaped object completely. This polyhedron was discovered by the Hungarian mathematician Lajos Szilassi in 1977.

 Eduardo Barbero Corral Spanish Ministry of Education , Social Afairs and Sport. Year 2007