Zometool - 5 cell


Here we describe how to build a so-called vertex-first projection of the 5 cell, one of the six regular polytopes in 4-dimensional space, using the zometool system. For the jumbo model you need

  • 5 balls,
  • 5 long yellow (y2) struts,
  • 6 long green (g2) struts.

Of course one can scale down the model to y1-g1 (medium size) or even to y0-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 the yellow struts to build the yellow skeleton, which has one central vertex and four further vertices at the loose ends.

Step 2

Connect these vertices using the green struts.

The model is now complete and you can see all five tetrahedral projected cells. Namely, there are four squashed tetrahedra surrounding the central vertex (with yellow and green edges) as well as the outer tetrahedron (with only green edges) containing these four central tetrahedra.

We remark that the vertex-first projection constructed here coincides with the cell-first projection of the 5 cell. The outer green tetrahedron corresponds to the closest cell, while the adjacent cells are projected to the yellow-green interior tetrahedra.