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How to build polyhedra with paper and rubber bands
Cheap and simple technique to build a lot of polyhedra. Snub cube
In Dürer's book 'Underweysung der Messung' the author published the first plane net of polyhedra, for example, this snub cube: ![]() ![]() Dodecahedron
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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 .
![]() ![]() Cuboctahedron
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A cuboctahedron is an Archimedean solid. It can be seen as made by cutting off the corners of an octahedron.
![]() ![]() ![]() Icosidodecahedron
![]() Truncated Tetrahedron
![]() ![]() Durer was the first who publish a plane net of a truncated tetrahedron: ![]() Truncated Cube
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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: This is the plane net of a truncated cube: Icosahedral lamp
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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: ![]() More: dannish lamp (IQlight):
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.
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Italian designer Bruno Munari conceived 'Acona Biconbi' as a work of sculpture. It is also a beautiful game to play with colors and shapes.
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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.
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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.
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Material for a session about polyhedra (Zaragoza, 23rd Octuber 2015) . Building a cube with cardboard and an origami octahedron.
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Material for a session about polyhedra (Zaragoza, 21st October 2016). Instructions to build several geometric bodies.
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Some properties of this platonic solid and how it is related to the golden ratio. Constructing dodecahedra using different techniques.
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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 .
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A cuboctahedron is an Archimedean solid. It can be seen as made by cutting off the corners of a cube.
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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.
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We study different cylinders and we can see how they develop into a plane. Then we explain how to calculate the lateral surface area.
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