matematicas visuales visual math
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:

Resources: Building polyhedra gluing faces
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:

Building polyhedra using cardboard discs | matematicasVisuales

You can download and print this template:

Taller Talento Matemático Zaragoza: desarrollo del cubo para descargar, download cube | matematicasVisuales

Building polyhedra using cardboard discs | matematicasVisuales

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

Building polyhedra using cardboard discs | matematicasVisuales

We can use different colors and play with textures:

Building polyhedra using cardboard discs | matematicasVisuales

More polyhedra:

Building polyhedra using cardboard discs | matematicasVisuales

Using paper we can build a beautiful lamp:

Building polyhedra using cardboard discs | matematicasVisuales
Building polyhedra using cardboard discs | matematicasVisuales
Building polyhedra using cardboard discs | matematicasVisuales
Building polyhedra using cardboard discs | matematicasVisuales

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

Resources: The golden rectangle and the icosahedron
With three golden rectangles you can build an icosahedron.
Resources: Building Polyhedra with cardboard (Plane Nets)
Using cardboard you can draw plane nets and build polyhedra.
Resources: How to build polyhedra using paper and rubber bands
A very simple technique to build complex and colorful polyhedra.
Resources: Modular Origami
Modular Origami is a nice technique to build polyhedra.
Resources: Building polyhedra using tubes
Examples of polyhedra built using tubes.
Resources: Tensegrity
Examples of polyhedra built using tensegrity.
Resources: Building polyhedra using Zome
Examples of polyhedra built using Zome.
Building polyhedra. Basic techniques: Taller de Talento Matemático de Zaragoza (Spanish)
Material for a sesion about polyhedra (Zaragoza, 13th Abril 2012).
Construcción de poliedros. Cuboctaedro y dodecaedro rómbico: Taller de Talento Matemático de Zaragoza 2014 (Spanish)
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.
Cube, octahedron, tetrahedron and other polyhedra: Taller de Talento Matemático Zaragoza,Spain, 2014-2015 (Spanish)
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.
Duality: cube and octahedron. Taller de Talento Matemático de Zaragoza, Spain. 2015-2016 XII edition (Spanish)
Material for a sesion about polyhedra (Zaragoza, 23rd Octuber 2015) . Building a cube with cardboard and an origami octahedron.
The Cuboctahedron and the truncated octahedron. Taller de Talento Matemático de Zaragoza, Spain. 2016-2017 XIII edition (Spanish)
Material for a sesion about polyhedra (Zaragoza, 21st October 2016). Instructions to build several geometric bodies.
The icosahedron and its volume
The twelve vertices of an icosahedron lie in three golden rectangles. Then we can calculate the volume of an icosahedron
The volume of the tetrahedron
The volume of a tetrahedron is one third of the prism that contains it.
Plane developments of geometric bodies: Tetrahedron
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 .
Regular dodecahedron
Some properties of this platonic solid and how it is related to the golden ratio. Constructing dodecahedra using different techniques.
Plane developments of geometric bodies: Dodecahedron
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 .
Plane developments of geometric bodies: Octahedron
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 .
Plane developments of geometric bodies: Tetrahedron
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 .