Cylinder (finite)
Infinite cylinders can be supported by having a torus of size 0 on one of the two axes. However, finite cylinders are not a possibility.
In a finite cylinder, two opposite faces would be connected to each other, as is done in a torus. The other two opposite faces would act as sharp boundaries, like in the "Plane" topology.
The letter used to denote these isn't exactly easy to come up with: C for Cylinder is already taken for cross-surface, and T for Tube is taken for torus. The third option, which I'll use for now unless someone can come up with something better (I considered R for Ring but it seemed too forced), is A for Annulus.
A * would be neccessary for one of the two bounds, which would indicate which of the two sets of opposite faces would be connected. This is the same notation used to determine which of the sets of faces is twisted on a Klein bottle.
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x = 92, y = 44, rule = B3/S23
71bo$71b2o$2b40o10b40o$2bo38bo10bo18b2o18bo$2bo38bo10bo18bo19bo$2bo38b
o10bo38bo$2bo38bo10bo38bo$2bo38bo10bo38bo$2bo38bo10bo38bo$2bo38bo10bo
38bo$2bo38bo10bo38bo$2bo38bo10bo38bo$2bo38bo10bo38bo$2bo38bo10bo38bo$
2bo38bo10bo38bo$2bo38bo10bo38bo$2bo38bo10bo38bo$2bo38bo10bo38bo$2bo26b
obo9bo10bo20bobo15bo$2bo11b3o9bo3bo10bo10bo11b3o7bo3bo12bo$2bo10bo3bo
8bo2bobo9bo10bo10bo3bo5bobo2bo12bo$b3o9b5ob3o4b3o11b3o9bo10b5ob3o6b3o
10bo$5o8bo3bobobo4bobo10b5o8bo10bo3bobobo6bobo10bo$2bo10bo3bob4obob3o
12bo10bo10bo3bob4o3bob3o10bo$2bo21bo16bo10bo23bo14bo$2bo38bo10bo38bo$
2bo38bo10bo38bo$2bo38bo10bo38bo$2bo38bo10bo38bo$2bo38bo10bo38bo$2bo38b
o10bo38bo$2bo38bo10bo38bo$2bo38bo10bo38bo$2bo38bo10bo38bo$2bo38bo10bo
38bo$2bo38bo10bo38bo$2bo38bo10bo38bo$2bo38bo10bo38bo$2bo38bo10bo38bo$
2bo38bo10bo18bo19bo$2bo38bo10bo18b2o18bo$2b40o10b40o$71b2o$71bo!
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x = 30, y = 32, rule = extendedlife:T30,32
30E16$16.4A$15.A3.A$19.A$15.A2.A3$6.3A$5.A2.A$8.A$8.A$5.A.A5$30E!
This is a similar case to the cylinder above, in which two opposite faces are connected, and the other two are solid boundaries. The difference here is that the two connected faces are inverted, like is seen on Klein bottles and cross-surfaces.
It seems that the letter M is unused for bounded grids so far, meaning it's free to use for this new topology.
Again, a * would be needed to determine which of the two sets of faces have a connection.
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x = 92, y = 44, rule = B3/S23
72bo$71b2o$2b40o10b40o$2bo38bo10bo18b2o18bo$2bo38bo10bo19bo18bo$2bo38b
o10bo38bo$2bo38bo10bo38bo$2bo38bo10bo38bo$2bo38bo10bo38bo$2bo38bo10bo
38bo$2bo38bo10bo38bo$2bo38bo10bo38bo$2bo38bo10bo38bo$2bo38bo10bo38bo$
2bo38bo10bo38bo$2bo38bo10bo38bo$2bo38bo10bo38bo$2bo38bo10bo38bo$2bo10b
o3bo11bobo9bo10bo10bo3bo5bobo15bo$2bo10b2ob2o8bo3bo10bo10bo10b2ob2o6bo
3bo12bo$2bo10bobobo8bo2bobo9bo10bo10bobobo5bobo2bo12bo$5o8bo3bob3o4b3o
11b3o9bo10bo3bob3o6b3o10bo$b3o9bo3bobobo4bobo10b5o8bo10bo3bobobo6bobo
10bo$2bo10bo3bob4obob3o12bo10bo10bo3bob4o3bob3o10bo$2bo21bo16bo10bo23b
o14bo$2bo38bo10bo38bo$2bo38bo10bo38bo$2bo38bo10bo38bo$2bo38bo10bo38bo$
2bo38bo10bo38bo$2bo38bo10bo38bo$2bo38bo10bo38bo$2bo38bo10bo38bo$2bo38b
o10bo38bo$2bo38bo10bo38bo$2bo38bo10bo38bo$2bo38bo10bo38bo$2bo38bo10bo
38bo$2bo38bo10bo38bo$2bo38bo10bo18bo19bo$2bo38bo10bo18b2o18bo$2b40o10b
40o$71b2o$71bo!
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x = 30, y = 32, rule = extendedlife:K30,32*
30E12$15.A2.A$19.A$15.A3.A$16.4A7$6.3A$5.A2.A$8.A$8.A$5.A.A5$30E!
Spheres are also one of the topologies of bounded grids which are supported. The following are two ways to make a sphere, which can be considered mirror images of each other.
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x = 94, y = 44, rule = B3/S23
20bobo48bobo$20b4o46b4o$2b40o10b40o$2bo17b4o17bo10bo17b4o17bo$2bo17bob
o18bo10bo18bobo17bo$2bo38bo10bo38bo$2bo38bo10bo38bo$2bo38bo10bo38bo$2b
o38bo10bo38bo$2bo38bo10bo38bo$2bo38bo10bo38bo$2bo38bo10bo38bo$2bo38bo
10bo38bo$2bo38bo10bo38bo$2bo38bo10bo38bo$2bo38bo10bo38bo$2bo38bo10bo
38bo$2bo38bo10bo38bo$2bo15b4o19bo10bo14b4o5bobo12bo$2bo14bo23bo10bo13b
o10bo13bo$5o12b3o21bo10bo13b3o7bobo10b5o$b3o15b3ob3o13b5o6b5o13b3ob3o
15b3o$5o16bobobo14b3o8b3o16bobobo14b5o$b3o13b4o2b4o14bo10bo13b4o2b4o
14b3o$2bo38bo10bo38bo$2bo38bo10bo38bo$2bo38bo10bo38bo$2bo38bo10bo38bo$
2bo38bo10bo38bo$2bo38bo10bo38bo$2bo38bo10bo38bo$2bo38bo10bo38bo$2bo38b
o10bo38bo$2bo38bo10bo38bo$2bo38bo10bo38bo$2bo38bo10bo38bo$2bo38bo10bo
38bo$2bo38bo10bo38bo$2bo38bo10bo38bo$2bo18bo19bo10bo19bo18bo$2bo18b2o
18bo10bo18b2o18bo$2b40o10b40o$21b2o48b2o$21bo50bo!
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x = 30, y = 30, rule = B3/S23:S30
bo2$bobo2$3bobo23bo2$5bobo2$7bobo2$9bobo2$11bobo2$13bobo2$15bobo2$17bo
bo2$19bobo2$21bobo2$o22bobo$o$o24bobo2$4bo22bobo$4bo!
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x = 30, y = 30, rule = B3/S23:S30
28bo2$26bobo2$o23bobo2$22bobo2$20bobo2$18bobo2$16bobo2$14bobo2$12bobo
2$10bobo2$8bobo2$6bobo2$4bobo22bo$29bo$2bobo24bo2$obo22bo$25bo!
As was proposed in the image, I'd suggest that the other form of the sphere be added simply by appending a * to the number, in which case the right hand version of the sphere mapping would be used. When run on this grid, the second pattern would work identically to the first.