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# Szilassi Polyhedron

Szilassi polyhedrons have a special topology.

## How it works

Pick one face (i.e., choose a number) and find how many neighbouring faces it directly touches.

## Things to try or ask around the exhibit

If you had a cube with six faces (such as dice), does one of its faces directly touch all five remaining faces?

## Background

Think of a cube (such as a die), with six faces. If you pick one face of a cube, the selected face directly touches four neighbouring faces, but it cannot touch all five remaining faces in the cube.

The Szilassi polyhedron is constructed from seven hexagonal faces, but its unique topological quality is that each face within the shape directly touch every other face within the shape. Similar to a tetrahedron, each face in a Szilassi polyedron directly touches all other faces in the polyhedron. So while one face of a six-faced cube touches four neighbouring faces, one face of the seven-faced Szilassi polyhedron is able to touch all six remaining faces.

## Finding the science in your world

The mathematical branch of topology can be used to explore why objects deform or pack together in certain ways. By understanding the mathematical properties of shapes, greater efficiencies can be found when packing objects for storage or transport.