Unfolding Polyhedra

Geometry Level 4

In geometry, a net of a polyhedron is an unfolding of the surface of the polyhedron produced by cutting the solid along some of its edges and flattening it into a polygon in the plane.

A net of a regular dodecahedron A net of a regular dodecahedron

How many different nets of a cube are there if reflections of the net are considered same?


The answer is 11.

Brian Lie by Brian Lie , 26, China

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1 solution

Brian Lie
May 17, 2019

The eleven nets of a cube The eleven nets of a cube

2 Helpful 3 Interesting 0 Brilliant 0 Confused

This is assuming that reflections of the net are the same. Two of these nets have a line of symmetry, while the other nine do not. If we allow mirror images as distinct nets, there are 20 20 possible nets.

Mark Hennings - 2 years ago

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Thank you. I editted it accordingly.

Brian Lie - 2 years ago

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