In this page we are going to explore a simple material to build beautiful polyhedra.

We can cut discs made of cardboard or paper and build polyhedra gluing these discs.

Very similar to this technique:

Using cardboard you can build beautiful polyhedra cutting polygons and glue them toghether. This is a very simple and effective technique. You can download several templates. Then print, cut and glue: very easy!

Our first example is a truncated icosahedron.

This is the result using five colors:

You can download and print this template:

Using five different colors we can build an icosahedron in which each vertex has these five colors:

REFERENCES

H.S.M. Coxeter - 'Introduction to Geometry', Wyley.

Hilber y Cohn-Vossen - "Geometry and the Imagination", AMS Chelsea Pub.

Magnus Wenninger - 'Polyhedron Models', Cambridge University Press.

Hugo Steinhaus - Mathematical Snapshots - Oxford University Press - Third Edition (p. 197)

Peter R. Cromwell - 'Polyhedra', Cambridge University Press, 1999.

H.Martin Cundy and A.P. Rollet, 'Mathematical Models', Oxford University Press, Second Edition, 1961 (p. 87).

W.W. Rouse Ball and H.S.M. Coxeter - 'Matematical Recreations & Essays', The MacMillan Company, 1947.

MORE LINKS

With three golden rectangles you can build an icosahedron.

Using cardboard you can draw plane nets and build polyhedra.

A very simple technique to build complex and colorful polyhedra.

Modular Origami is a nice technique to build polyhedra.

Examples of polyhedra built using tubes.

Examples of polyhedra built using tensegrity.

Examples of polyhedra built using Zome.

Material for a sesion about polyhedra (Zaragoza, 13th Abril 2012).

Material for a sesion about polyhedra (Zaragoza, 9th May 2014). Simple techniques to build polyhedra like the tetrahedron, octahedron, the cuboctahedron and the rhombic dodecahedron. We can build a box that is a rhombic dodecahedron.

Material for a sesion about polyhedra (Zaragoza, 7th November 2014). We study the octahedron and the tetrahedron and their volumes. The truncated octahedron helps us to this task. We build a cubic box with cardboard and an origami tetrahedron.

Material for a sesion about polyhedra (Zaragoza, 23rd Octuber 2015) . Building a cube with cardboard and an origami octahedron.

Material for a sesion about polyhedra (Zaragoza, 21st October 2016). Instructions to build several geometric bodies.

The twelve vertices of an icosahedron lie in three golden rectangles. Then we can calculate the volume of an icosahedron

The volume of a tetrahedron is one third of the prism that contains it.

The first drawing of a plane net of a regular tetrahedron was published by Dürer in his book 'Underweysung der Messung' ('Four Books of Measurement'), published in 1525 .

Some properties of this platonic solid and how it is related to the golden ratio. Constructing dodecahedra using different techniques.

The first drawing of a plane net of a regular dodecahedron was published by Dürer in his book 'Underweysung der Messung' ('Four Books of Measurement'), published in 1525 .

The first drawing of a plane net of a regular octahedron was published by Dürer in his book 'Underweysung der Messung' ('Four Books of Measurement'), published in 1525 .

The first drawing of a plane net of a regular tetrahedron was published by Dürer in his book 'Underweysung der Messung' ('Four Books of Measurement'), published in 1525 .