The Zome Model of the First Stellation of the 120-Cell, page 8


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19. Make 60 of the assemblies as shown, using 2 balls, 1 short red, 2 medium reds, and 2 medium yellows. The shape of this piece is not intuitive and it is certainly not easy to describe, so you should study the photo carefully. Perhaps it looks like a model airplane, or maybe a walking stick, or maybe just a stick. Notice that the three red struts all lie on the same line with the short strut between the two mediums. The two yellows intersect this line in two acute angles, and they are separated from each other by an obtuse angle. This assembly should have a single plane of reflection symmetry. This uses 120 balls, 60 short reds, 120 medium reds, and 120 medium yellows.

20. Mount these 60 twigs as shown. Again, the way that each is attached is not intuitive, so one should examine the photo carefully (confusing as it may appear). Notice in the photo that the three red collinear struts serve to connect between a black ball and a green ball. The yellow struts should also naturally attach to the model, so, in case they don't, it may be necessary to reverse the orientation of the assembly. Notice that the medium yellows attach at the false vertices of the large blue pentagrams constructed earlier.

This is how the model should appear after you complete step 20. At this point you should observe that the entire model is now bounded by another, larger, red rhombic triacontahedron.

21. At this point, notice that in the previous step there were 60 balls which seemed to serve no purpose. These connected a short red to a medium red so that the two struts were collinear. We now use these 60 balls, connecting them together with 60 medium blues, forming a total of 12 B2 pentagons. Notice that these medium blues, assuming they represent straight line segments, must intersect with some long blues attached earlier. Unless you have half-blues, there's no way to avoid this and have all edges of this polychoron faithfully represented. In the model shown, each long blue strut is bent slightly to allow a medium blue to connect, with the medium blue on the "outside".


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