Build your own Polyhedra

Compiled by Paul Bourke and Matt Storz

Based upon software called "Shapescape" (previously known as "Flatland") written by Matt Storz.


The following provides outlines of the faces of many polyhedra in a form suitable for printing. The outlines can then be cut, folded, and glued so as to create real models. The images are supplied in two formats, GIF and Postscript. If you have a display Postscript system or have software that can read and manipulate Postscript then that is the best format to use. Otherwise most image editors will accept GIF, indeed unless you wish to resize the model you should be able to print the GIF version directly from your browser.

Table of Polyhedra

Name  GIF   PostScript      Example 
Cube * *  
Snub Cube * *  
Truncated Cube * *  
Tetrahedron * *  
Truncated Tetrahedron * *  
Octahedron * *  
Cube Octahedron * *  
Rhombic Cube Octahedron * *  
Truncated Octahedron * *  
Truncated Cube Octahedron * *  
Icosahedron * *  
Truncated Icosahedron * *  
Dodecahedron * *  
Icosi Dodecahedron * *  
Truncated Dodecahedron * * *
Rhombic Dodecahedron * *  
Truncated Icosi Dodecahedron * * *
Rhombic Icosi Dodecahedron * *  
Rhombic Triacontahedron * * *

Description of Flatland by Matt Storz

Flatland is a Windows program that allows various 3D shapes, polyhedra, to be created and then flattened so that a pattern can be printed to make a model of the polyhedron. program (octahedron, dodecahedron, icosahedron, etc) to start with. These polyhedra can be manipulated in various ways to produce more complicated shapes. After selecting a polyhedron, it can be rotated and viewed from every side. Pictures and colours can be applied to each face of the polyhedron. The polyhedron can then be flattened and printed out on one or more sheets of paper which can then be used as a template to cut cardboard to produce a model of the polyhedron.

Comments by others on building the models

By Matt Storz

Here's how I make the models... I use Avery full sheet label paper with a color ink jet printer. I printout the model net from the flatland software, I place the labels on regular cardboard that I pick up at my local grocery store. I use an exacto knife and a metal straight edge along with a cutting mat to cut out the net. I score all of the fold lines with the exacto knife. I fold and tape all of the seams with just regular transparent tape until I can't get my hands into the inside of the polyhedron model. Then I use paper glue to connect the last seam. I've tried a few kinds of glue and the best I've found so far is the glue stick kind.. You just rub it on the two paper edges and it sticks together pretty quickly and its fairly strong too.

By Simon Bullen

This is what I've been doing with polyhedra constructed with plans from "Numerical Recipes":

  • laser-print the plans directly onto manilla folder
  • glue and tape the model together ensuring that all the tabs are on the *outside*, leaving one face of the model open.
  • place a wick through the centre of the opposite face to the open one
  • fill with molten wax in a variety of stages and colours - polyhedra candles! :-)


  • Sticky-tape and glue will often lose their adhesiveness when the model is filled with hot wax - let the wax cool and thicken slightly before filling the model. This keeps the tape happy, and the wax is less likely to find its way through small holes
  • be prepared to make a mess!
  • tessellated polyhedra produce fantastic candles, but the models take quite a bit longer to make
  • you need to destroy the mould to get the candle out - don't lose your original designs!

If you have suggestions or practical ideas on creating physical models we'd like to hear from you.