Here we describe how to build a cell-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

  • 8 balls,
  • 6 long blue (b2) struts,
  • 6 long green (g2) struts.

Of course one can scale down the model to b1-g1 (medium size) or even to b0-g0 (mini version).

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

The pictures below were taken by Eva-Maria Gassner.

Step 1

Use 12 of the green struts and 6 of the balls to build a regular octahedron. This will be the central cell of the projection.

Step 2

Use 16 blue struts, 8 green struts and 8 balls to build a type of cuboid around the octahedral cell.

Step 3

Use the remaining struts and balls to build four copies of a roof that are mounted on each of the big sides of the cuboid. The model is now complete.

This zometool model of the 24 cell shows the central octahedral cell, which has two pre-images. For each of its faces 8 another octahedral cell that appears squashed as a result of the projection. Again, each of these cells has two pre-images. Finally, one can see 6 flat octahedra as blue crosses on the boundary of the model. This yields (1+1)+(8+8)+6 = 24 octahedral cells in total.