I have one of these and it is a pretty cool plant. It gets hours of daily sun where it's located here (outside year round) but the overhead protection kicks in during the summer to reduce the more intense overhead rays.
These plants are male or female and you need two of them (male and female) to make more. The plant in the picture above is male. Like other Euphorbias you have to harvest the fruit right before it explodes or you lose the seeds. You can also try to bag it if you aren't going to be there at the right time.
They also hybridize with other similar Euphorbias and I have seen some pretty attractive polygona hybrids for sale. It's not hard to pick up some pollen on a fine paintbrush (the yellow dots on the male flowers above, falling onto the body of the plant below it) and transfer that to a female plant to see what happens.
In old age they become more tall than wide, less and less like a baseball over time. This is different from the etiolated growth you sometimes see in pictures, where the top part is narrower than the bottom part. A mature E. obesa grows like a column with a rounded top.
Try to provide strong light so that you avoid etiolation, especially since the main appeal of the plant is its form. You will read that this plant is sensitive to rot, and no doubt it will respond poorly to too much water, but I tend not to worry so much about that with strong light, excellent drainage, and a relatively small pot. I water this plant like most of my other succulents. You do want to be careful with cold and dark conditions during winter, like most other succulents.
I have seen some pretty ancient plants in small pots, so you don't need to provide lots of space. I try to use a pot that's just wider than the body of the plant. I'm guessing my plant will end up in a 6 inch pot as its final home.
Some of these plants offset at the base, and I'm not sure if that's due to some hybrid character or actually just the variation of the species. Either way it's not a bad look.
One thing that's kind of fun is each plant has its own pattern of banding in between the ribs. Some of them can be colorful. This texture is probably something you can pick up at a very young age, and it imparts quite a bit of character.