Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. It's 100% free, no registration required.

Sign up
Here's how it works:
  1. Anybody can ask a question
  2. Anybody can answer
  3. The best answers are voted up and rise to the top

Here's the 57-cell in vZome with lots of strut crossings:

57-cell in vZome

Is it possible to construct the 57-cell in vZome without any strut crossings? That is, 57 nodes, 171 struts, in the 57-cell / Perkel graph configuration, with no struts going through other struts or clipping nodes?

A Mathematica version is at 57-cell. The vZome version is at 57cell.vZome.

I'll pay $57 for the first solution with no trickery of any kind. All of the strut-types currently defined in vZome are allowable.

share|cite|improve this question
Surely just making the nodes and struts thin enough and randomly moving the nodes around a little ought to yield a solution. Of course, that's sort of a cheap trick, in the sense that the result won't have any kind of elegant symmetry and won't be much help in, say, constructing a nice-looking physical model. – Ilmari Karonen Oct 2 '11 at 3:31
Zome is based on Phi-space, where all coordinates are triples of the form $a + b\phi $. With 57 nodes and the restriction to defined vZome directions, there are only a finite (but huge) number of available lattice points, and randomly moving the nodes won't work. – Ed Pegg Oct 2 '11 at 4:53

Your Answer


By posting your answer, you agree to the privacy policy and terms of service.

Browse other questions tagged or ask your own question.