The regular pentagon can't tessellate the plane
The angle of the regular pentagon doesn’t divide 360°: you can’t tessellate the plane using only regular pentagons.
This very figure can be used also to show why there are only five regular polyhedra: regular pentagons can be used as faces of a polyhedron only by putting three of them around a vertex (in this way you get the dodecahedron).
The image has been realised for the exhibition Simmetria, giochi di specchi - Symmetry, playing with mirrors.
© matematita
The image belongs to the sections...:
Other tessellations (2D geometry)
All together (3D geometry)
