A Curiosity

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

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