When we use Zometool to construct 3-D projections of 4-D polytopes, we almost always find places where the projected edges intersect. This is only an artifact of the projection, of course. Since we want the Zome balls to represent actual vertices of the 4-D polytope, we don’t want to use them for these intersections, which are NOT vertices at all. With the availability of 3-D printing, we have an alternative:

This design is meant to be 3-D printed in color, to be used where red and yellow struts intersect in the Triality projection of the 24-cell, shown below.

You can purchase these cross-connectors from Shapeways, as a group of six joined together. This keeps the per-part cost down to about $1.50 US. There is no markup charged for any items in the vZome Shapeways store.

Remember, you’ll need two sets, for 12 total, to model the 24-cell projection shown above.

For your convenience, I’m also sharing the STL and DAE files, for both the single connector and the gang of six. (DAE files include color information, which might be useful if these can ever be color printed economically.)