A node-and-strut construction system.

Zome System is a unique 31-zone system that takes ball-and-stick construction to its highest level. Available in kits of various sizes, Zome System is a powerful design tool and educational toy for kids (ages 6 and up), hobbyists, students, teachers and researchers. Precision-molded in ABS plastic, Zome System models spatial structures representing hyperspaces of up to 31 dimensions, geodesic space-frame structures and molecular models, including quasicrystals and Fullerenes.

Zometool, Inc.
1526 South Pearl Street - Denver, CO 80210 USA
Toll-free: 888-966-3386 - Phone: 303-733-2880 - Fax: 303-733-3116

I tried one of their introductory kits (bought it out of a new-agey mailorder catalog, of all places) and I'm hooked. I just ordered their Advanced Math Creator Kit & Geometry Book combination, which includes green struts which give you extra directions and the ability to make all the platonic solids.