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5 Cube Zones 3D Model
A sequence of polyhedra illustrating the 5 cubic, or cartesian systems inherent in icosahedral
symmetry. In this sequence, the zonal aspect of the cubic systems is shown. In the largest
polyhrdron, the 6 square faces of one cubic system are connected to each other by bands
of rhombic facets shown in green, with edges parallel to the squares. Each band is a zone
which can have it’s width adjusted independently of the rest of the assembly. In this case, all
3 of the zones colored green can act as a group, a triple zone with an octahedroid form.
Reducing this whole triple zone to zero width leaves the second largest polyhedron, showing
the red cubic system with it’s associated zone. Reducing the red triple zone to zero width
leaves a polyhedron showing the blue triple zone. Reducing this to zero width leaves a polar
triacontahedron, which is composed of the 2 remaining cartesian systems. Finally, the orange
triple zone is reduced to zero width, leaving a single purple cube.