matematicas visuales visual math
How to build polyhedra with paper and rubber bands

Cheap and simple technique to build a lot of polyhedra.

Resources, How to build polyhedra with paper and rubber bands: Download, print, cut and build | matematicasVisuales
Resources, How to build polyhedra with paper and rubber bands: Download, print, cut and build | matematicasVisuales
Resources, How to build polyhedra with paper and rubber bands: Download, print, cut and build | matematicasVisuales
Resources, How to build polyhedra with paper and rubber bands: Download, print, cut and build | matematicasVisuales
Resources, How to build polyhedra with paper and rubber bands: Download, print, cut and build | matematicasVisuales
Resources, How to build polyhedra with paper and rubber bands: Download, print, cut and build | matematicasVisuales
Resources, How to build polyhedra with paper and rubber bands: Download, print, cut and build | matematicasVisuales
Resources, How to build polyhedra with paper and rubber bands: Download, print, cut and build | matematicasVisuales
Download, print, cut and build.
Snub cube

In Dürer's book 'Underweysung der Messung' the author published the first plane net of polyhedra, for example, this snub cube:

Resources, How to build polyhedra with paper and rubber bands: Durer's snub cube plane net | matematicasVisuales
Resources, How to build polyhedra with paper and rubber bands: snub cube plane net | matematicasVisuales
Dodecahedron
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 .
Resources, How to build polyhedra with paper and rubber bands: dodecahedron plane net| matematicasVisuales
Resources, How to build polyhedra with paper and rubber bands: dodecahedron| matematicasVisuales
Cuboctahedron

The volume of a cuboctahedron (II)
A cuboctahedron is an Archimedean solid. It can be seen as made by cutting off the corners of an octahedron.
Volume of a cuboctahedron: a cuboctahedron made with rubber bands and paper | matematicasvisuales
Volume of a cuboctahedron: a cuboctahedron and a octahedron made with rubber bands and paper | matematicasvisuales
Volume of a cuboctahedron: plane net of a cuboctahedron made with rubber bands and paper | matematicasvisuales
Icosidodecahedron
Resources, How to build polyhedra with paper and rubber bands: Icosidodecahedron | matematicasVisuales
Truncated Tetrahedron
Truncated tetrahedron
The truncated tetrahedron is an Archimedean solid made by 4 triangles and 4 hexagons.
Resources, How to build polyhedra with paper and rubber bands: Truncated tetrahedron | matematicasVisuales
Resources, How to build polyhedra with paper and rubber bands: Truncated tetrahedron | matematicasVisuales
Resources, How to build polyhedra with paper and rubber bands: Truncated tetrahedron | matematicasVisuales

Durer was the first who publish a plane net of a truncated tetrahedron:

Resources, Durer  was the first to publish a plane net of a truncated tetrahedron | matematicasVisuales
Truncated Cube
Truncations of the cube and octahedron
When you truncate a cube you get a truncated cube and a cuboctahedron. If you truncate an octahedron you get a truncated octahedron and a cuboctahedron.

You need six octogons and eight equilateral triangles:

Truncated cube: You need six octogons and eight equilateral triangles | matematicasVisuales

This is the plane net of a truncated cube:

Truncated cube: plane net | matematicasVisuales
Truncated cube: | matematicasVisuales
Truncated cube: | matematicasVisuales
Truncated cube: build using cardboard and rubber bands | matematicasVisuales
Icosahedral lamp
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

Very easy icosahedral lamp built with cardboard and rubber bands:

Construcción poliedros| Lámpara icosaedro con gomas  | matematicasVisuales
Construcción poliedros| Lámpara icosaedro con gomas: descargar plantilla | matematicasVisuales

More: dannish lamp (IQlight):

Construcción poliedros| lámpara IQLight | matematicasVisuales

This model was designed by Holger Strom and it is called IQlight. It is based in the rhombic triacontahedon.

REFERENCES

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: Building polyhedra gluing discs
Simple technique to build polyhedra gluing discs made of cardboard or paper.
Resources: Acona Biconbi, designed by Bruno Munari
Italian designer Bruno Munari conceived 'Acona Biconbi' as a work of sculpture. It is also a beautiful game to play with colors and shapes.
Resources: The golden rectangle and the icosahedron
With three golden rectangles you can build an icosahedron.
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 session about polyhedra (Zaragoza, 13th Abril 2012).
Construcción de poliedros. Cuboctaedro y dodecaedro rómbico: Taller de Talento Matemático de Zaragoza 2014 (Spanish)
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.
Cube, octahedron, tetrahedron and other polyhedra: Taller de Talento Matemático Zaragoza,Spain, 2014-2015 (Spanish)
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.
Duality: cube and octahedron. Taller de Talento Matemático de Zaragoza, Spain. 2015-2016 XII edition (Spanish)
Material for a session 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 session about polyhedra (Zaragoza, 21st October 2016). Instructions to build several geometric bodies.
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 .
The volume of a cuboctahedron
A cuboctahedron is an Archimedean solid. It can be seen as made by cutting off the corners of a cube.
Truncated tetrahedron
The truncated tetrahedron is an Archimedean solid made by 4 triangles and 4 hexagons.
Plane developments of geometric bodies (1): Nets of prisms
We study different prisms and we can see how they develop into a plane net. Then we explain how to calculate the lateral surface area.
Plane developments of geometric bodies (3): Cylinders
We study different cylinders and we can see how they develop into a plane. Then we explain how to calculate the lateral surface area.
Plane developments of geometric bodies (5): Pyramid and pyramidal frustrum
Plane net of pyramids and pyramidal frustrum. How to calculate the lateral surface area.
Plane developments of geometric bodies (7): Cone and conical frustrum
Plane developments of cones and conical frustum. How to calculate the lateral surface area.
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 .