Resources: Discs

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:

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

We can use different colors and play with textures:

More polyhedra:

Using paper we can build a beautiful lamp:

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.

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 session about polyhedra (Zaragoza, 13th Abril 2012).
Material for a session 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 session 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 session about polyhedra (Zaragoza, 23rd Octuber 2015) . Building a cube with cardboard and an origami octahedron.
Material for a session about polyhedra (Zaragoza, 21st October 2016). Instructions to build several geometric bodies.
Microarquitectura is a construction game developed by Sara San Gregorio. You can play and build a lot of structures modelled on polyhedra.
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 .