Components and Nets of Regular Polyhedra

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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



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.


[1] C. Palmer. 27 Blue Dihedral Kaleidos [Video]. (Jun 2, 2016)

[2] J. Richter-Geberrt. Four Mirrors and a Rod—MathLapse [Video]. (Jun 2, 2016)

[3] Roe Goodman's Home Page, Three-Dimensional Kaleidoscopes,

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