A Zometool model of an 8 cell

Here we describe how to build a vertex-first projection of the 8 cell, one of the six regular polytopes in 4-dimensional space, using the zometool system. For the model you need

  • 15 balls,
  • 28 long yellow (y2) struts.

Of course one can scale down the model to y1 (medium size) or to 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

Use the 4 yellow struts to build the yellow skeleton, which has one central vertex.

Step 2

Build 4 yellow stars and mount them on the loos ends of the struts constructed in step 1.

Step 3

Use balls to connect loose struts.

Step 4

Build another 4 yellow stars and use them to connect the balls constructed in step 3. Four yellow parallelotopes must arise and the model is complete.

In the model you can see four parallelotopes surrounding the central vertex. In 4d these are cubes, but they have been squashed by the projection. Note that each of the four visible cells has two pre-images.