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I've tabulated 16 possible ways of creating different spherical coord systems, and attached an image below to demonstrate them all. They are all spheres, though the coordinate system is different for each one. Assume an orthographic projection.

Some are blanked out, since they are similar to the others but simply rotated, so essentially, there are 10 systems really in total.

System "I" is the one in common use, used for the geographical coord system (and effectively a rotation of the standard spherical coord system). For that one, all of the 'curved' vertical lines meet at the north and south pole (creating a terry's chocolate orange type effect), whilst all the straight horizontal lines are parallel with each other. On the other hand, something like system "G", has 4 of these points where all the lines meet (west and east sides, as well as the 2 usual north and south poles).

What I want to know is do some of the other nine systems have special names too (and what are they?). And why does (the rotated version of) system 'I' get exclusive access to the name of "spherical coords", when some of the others look just as interesting and useful (particularly systems A, B, D, and G which are more 'symmetric') ?

http://www.skytopia.com/stuff/sphere4.png [Broken]

Some are blanked out, since they are similar to the others but simply rotated, so essentially, there are 10 systems really in total.

System "I" is the one in common use, used for the geographical coord system (and effectively a rotation of the standard spherical coord system). For that one, all of the 'curved' vertical lines meet at the north and south pole (creating a terry's chocolate orange type effect), whilst all the straight horizontal lines are parallel with each other. On the other hand, something like system "G", has 4 of these points where all the lines meet (west and east sides, as well as the 2 usual north and south poles).

What I want to know is do some of the other nine systems have special names too (and what are they?). And why does (the rotated version of) system 'I' get exclusive access to the name of "spherical coords", when some of the others look just as interesting and useful (particularly systems A, B, D, and G which are more 'symmetric') ?

http://www.skytopia.com/stuff/sphere4.png [Broken]

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