The HemiSoccer Ball
Introduction. The polyhedron underlying the common soccer ball is a truncated icosahedron. It is an Archimedean solid consisting of 12 regular pentagons and 20 regular hexagons. One may make a model using Zome, using 90 identical blue struts and 60 connectors: 
One may also make a "hemisoccer ball". Abstractly, this is defined by identifying points on the soccer ball with their antipodes. This is essentially the same trick for obtaining the real projective plane from the 2dimensional sphere. Since the truncated octahedron is invariant under the antipode map, this is welldefined. The Zome model represents the 1dimensional skeleton of this polyhedron. 
Some Details. Two models appear in the stereogram. The first is a Zome model of the complete graph K_{6} on six vertices. The second is the hemisoccer ball. The complete graph K_{6} can be used as a guide for understanding or building the hemisoccer ball. Notice that K_{6} uses 6 distinctlycolored connectors. Each single vertex of K_{6} corresponds to a cluster of 5 connectors of the same color in the hemisoccer ball. Each commonly colored cluster is spanned by a nonplanar pentagon. These 6 pentagons (half the number of pentagons in the soccer ball) are connected to each other via corresponding edges of K_{6}. That is, for every edge of K_{6}, there is a pair of pentagons in the hemisoccer ball connected by an edge of that type. The hemisoccer ball also has 10 hexagons. By some small miracle, the hexagons in this model are all flat (affinely spanning only a 2dimensional space). The 57Cell. In the 1970's and 1980's, Coxeter and Grünbaum (and others) studied two selfdual abstract regular polytopes, known as the 11cell and the 57cell. The 1dimensional skeleton of the 11cell is simply the complete graph K_{11} on 11 vertices, so a faithful Zome model would be neither interesting nor possible to build. One may regard the hemisoccer ball as a "layer" of the 57cell. Specifically, given any vertex of the 57cell, there are precisely 30 vertices of distance 2 in the 1dimensional skeleton, and the connectivity of these vertices coincides with that of the hemisoccer ball. Linkless Embeddings of Graphs. The existence of a Zome model of the hemisoccer ball makes one wonder if it is possible to make then entire 1dimensional skeleton of the 57cell using Zome, although it seems highly doubtful. According to a theorem of Robertson, Seymour, and Thomas, a graph has a linkless embedding in R^{3} if and only if it does not have a minor belonging to the 7member Petersen Family. By construction, the Zome model of the hemisoccer ball has a member K_{6} as a minor. One would be able to say this about every vertex of the 57cell. Thus, a Zome model of the 57cell would have 57 different copies of the hemisoccer ball. This seems to be too many.... 
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