Well, it isn't actually a cactus. Rather, it is some species of Euphorbia. I'm not sure about the species, although chances are it is either E. ammak, E. acrurensis, or maybe even E. trigona.

Pruning one of these plants can prove challenging. All Euphorbias produce a thick white latex, that when you cut the plant, bleeds out. The latex is toxic, and usually a potent irritant. Getting any of the latex in your eyes or on mucus membrane will prove exceptionally painful, and in some cases, can cause permanent damage. Therefore, before you embark on a pruning such a large plant, donning some safety glasses, gloves, long sleeves and pants would be a good idea. This warning may seem a little extreme, and usually it is. However, some people are very sensitive while some plants are particularly potent. Given that, it is better to be safe than sorry, and to use the appropriate precautions.

With the requisite warning out of the way, you'll be pleased to learn that the actual pruning of these plants is straightforward. As you suspected, cutting at one of the joints is the easiest way to do, and will keep the plant looking more attractive. You can cut right across a stem, but it doesn't look as nice, and will bleed like mad. Keep a rag handy to wipe up the latex that bleeds out.

The last bit of advice I might offer, is to wait until spring to do any major pruning. I realize that since this is in an office, the spring won't be any warmer, but there will be more light. Pruning induces branching, and if there isn't much light (like winter in NY), then the new growth will be very leggy and tall, and not very healthy either.

I agree, take heed -- once after pruning my Euphorbia lactea I got some latex in my eye (by rubbing my eye after getting latex on hands). It was very painful and my eyelids swelled up! So I would wear gloves and protective eyewear!

Thanks for the advice & warnings.

The plant actually sits in a south facing window of a good size storefront, so it does get alot of light.

At least now I can also check up on some notes for proper care.

Thanks again~
C

For an indoor specimen, it actually looks pretty darn good to me. They will often grow much too fast for their own good in poor light, and will end up really drooping since they can't support themselves.

Dave makes a good point I forgot to mention. Wash your hands very, very thoroughly after handling any Euphorbias to avoid transferring the latex to somewhere sensitive.

Also, for those interested, the juice of Aeonium lindleyi is an effective antidote to Euphorbia latex. Squeeze some out onto the afflicted area, and you should feel relief in a few minutes. A. linleyi can be found on eBay occasionally, and at many specialty nurseries for only a few dollars.