Here we describe how to build a vertex-first projection of the 24 cell, one of the six regular polytopes in 4-dimensional space, using the zometool system. For the model you need

  • 15 balls,
  • 12 long blue (b2) struts,
  • 32 long yellow (y2) struts.

Of course one can scale down the model to b1-y1 (medium size) or to b0-y0 (mini version).

For further information and instructions you might also wish to consult one of the following webpages:

The pictures below were taken by Eva-Maria Gassner.

Step 1
Build 7 yellow lollipops and another yellow 'double' lollipop. Put them together to form a yellow star. The centre of this star is the central vertex of the projection.

Step 2
Use the blue struts to connect the loose yellow ends. The result is a star-burst cube.

Step 3
From the remaining struts build 6 yellow sputniks and mount them on the faces of the cube in order to complete the model.

This Zometool model of the 24 cell shows the 6 octahedral cells that surround the central vertex. Each of these cells has two pre-images and appears squashed as a result of the projection. The remaining 12 cells can be seen at the outer boundary of the model. They appear flat as yellow parallelograms together with a blue diagonal, since the are viewed in 4d under a 90 degree angle.