Components and Nets of Regular Polyhedra

Initializing live version
Download to Desktop

Requires a Wolfram Notebook System

Interact on desktop, mobile and cloud with the free Wolfram Player or other Wolfram Language products.

This Demonstration shows the five regular solids (or Platonic solids), a rhombic dodecahedron, and a rhombic triacontahedron. You can see a (possibly truncated) pyramid with vertex at the center of the polyhedron and base that is a face of the polyhedron. You can also see the fundamental region of a triangular pyramid. You can use a net to construct certain kaleidoscopes with three, four, or five mirrors.

Contributed by: Izidor Hafner (June 2016)
Open content licensed under CC BY-NC-SA


Snapshots


Details

The photograph shows a kaleidoscope made using a net of the truncated fundamental region of the regular icosahedron. The net is printed and metallic foil is glued to it.

References

[1] C. Palmer. 27 Blue Dihedral Kaleidos [Video]. (Jun 2, 2016) www.youtube.com/watch?v=rE7IWQtccbM.

[2] J. Richter-Geberrt. Four Mirrors and a Rod—MathLapse [Video]. (Jun 2, 2016) www.youtube.com/watch?v=zTS9SN18E58.

[3] Roe Goodman's Home Page, Three-Dimensional Kaleidoscopes, http://www.math.rutgers.edu/~goodman/pub/monthly.pdf



Feedback (field required)
Email (field required) Name
Occupation Organization
Note: Your message & contact information may be shared with the author of any specific Demonstration for which you give feedback.
Send