Here we describe how to build an edge-first projection of the 16 cell, one of the six regular polytopes in 4-dimensional space, using the zometool system. For the model you need

  • 6 balls,
  • 5 long blue (b2) struts,
  • 8 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

Use 4 of the blue struts to built a square.

Step 2

Mount a yellow pyramid on one side of the square.

Step 3

Add a blue strut emanating from the tip of the yellow pyramid that points to the other side of the square. This is the central edge of the projection.

Step 4

Complete the model by constructing another yellow pyramid as in step 2.

This Zometool model of the 16 cell shows an edge at the centre of the projection, which is surrounded by 4 tetrahedral cells. In 4d these are regular tetrahedra, but they appear squashed because of the projection. Each of these cells has two pre-images. Moreover, the remaining 8 cells appear as flat triangles on the boundary, since they are viewed under a 90 degree angle.