# Can the 57-cell be made in vZome without strut crossings?

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

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 $57 for the first solution with no trickery of any kind. All of the strut-types currently defined in vZome are allowable. - Surely just making the nodes and struts thin enough and randomly moving the nodes around a little ought to yield a solution. Of course, that's sort of a cheap trick, in the sense that the result won't have any kind of elegant symmetry and won't be much help in, say, constructing a nice-looking physical model. – Ilmari Karonen Oct 2 '11 at 3:31 Zome is based on Phi-space, where all coordinates are triples of the form$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