![]() At each toropole, the radius would be zero, thus degenerating into a circle, much like how a circle tracing out the surface of a sphere degenerates into a point at each pole. The rind of the glome is traced out as the sweep of a torus moving from the north toropole, through the yellow torus, through the toroquator, through the magenta torus to the south toropole. ![]() These two circles are actually the "poles", or toropoles of the glome - let's say the one in the yellow torus is the north toropole, and the other one, in the magenta torus, is the south toropole. Similarly, there is a line running vertically down the center of the yellow torus, which is really a circle, and there is another circle just outside the projection envelope (thus invisible) but which would be almost in the center of the magenta torus. This unmarked torus is actually the "toric equator", or toroquator. If you look hard enough, you can actually see one more torus between the yellow and purple ones, which has been squashed so much by the projection it looks more like a cylinder. These toruses are actually analogous to the lines of latitude in the sphere subdivision. In this subdivision, the two highlighted regions (yellow and magenta) are toruses. The second subdivision arranges the rind of the glome like that of a duocylinder: The curves of longitude stay as one-dimensional curves, but spread out in two dimensions instead of one: they connect the pole to all points on the "spheres of latitude". In the glome subdivision, the curves of latitude become spheres surrounding the pole, getting bigger and bigger until they reach the projection envelope. In the sphere diagram, we have two types of curves: those of latitude, which are the circles that surround the pole without touching it, and those of longitude, which are the circles which go through the pole and come out the other side. Here we can see the "pole" of the glome, the point in the middle near the top where all the curves converge, similar to the pole in the sphere diagram. The first is analogous to the second image above: There are two main subdivisions of the glome. The first diagram above shows a wireframe subdivision the second shows this subdivision projected into 2D with hidden surface removal performed. First, we'll show a subdivision of the sphere: We can visualize the glome by looking at subdivisions of it. ⇒ sphere of radius ( rcos(π n/2)) Visualization
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