Topologically, no. If you had a DunDo cup made out of silly putty, there’s no way you could stretch and mold it into a donut without poking a hole through it at some point.
For some reason, I always feel obliged to say something in threads like this. “Tori” is what I see most often as the plural used by mathematicians.
No, in the mathematical context, that’s not a hole, it’s quite different than the hole in a torus/donut. To a topologist, a paper cup might as well be a sphere. (Did I mention that I spill my coffee a lot?)
A paper cup is topologically equivalent to a jelly donut, though.
But did you ever try to drink coffee out of a jelly donut?
If it leaked from the bottom would that be torifaction?
We need an actor to help us with this.
Someone who has lots of TV experience.
Alex Trebek? Naaaah. Tori Spelling! 
In my world that would be called surgery. (Anecdote: When I was a grad student I roomed with some Med School students who were amused that I had a book on my shelf called Surgery on Simply-Connected Manifolds.)
Possibly also a tragedy:
*A mathematician is a machine for turning coffee into theorems. --*Alfréd Rényi
I always thought that was attributed to Erdos.
I will always say toruses. I once read in a style book that an -s or -es plural was never wrong. If we borrow a word from any language but Latin or Greek, we use an English plural. And if we use the Latin plural, why don’t we properly inflect it case. I consider tori an affectation, to be honest. Anyway, it is not a matter of prescription, but of description. Use whichever you like. Invariable plurals like deer (I would always say walruses) and irregular ones like children and historical vestiges, which cannot be the case with a loan word like torus.
Attributed to, but incorrectly, it seems. (See Wikipedia or Wikiquote.)
It may also be an affectation, but I use “tableaux” as the plural of tableau.
I had to use this at work: “toroids”.
One toroid is a ‘torus.’ Two toroids are . . . well, ‘toroids.’
Tripler
I am an engin[del]ear[/del] . . . an engin[del]ere[/del] . . . an engin[del]ier[/del] . . . I am good at math.
But a toroid is not necessarily a torus.
“Toroid”, as in “an object having the shape of a torus; a toroidal object” is an OK word, with plural “toroids” (what else would it be?) Cf. “asteroid.” Don’t confuse “toroidal” and “toric”
Toruses is correct.
See, that’s the problem and it leads to false plurals, like octopi and hippopotami.
Only dufi make those mistakes.
But many people do consider “tori” to be a gateway plural.
Not according to the Oxford English Dictionary, whereas the Oxford Dictionary of English allows it. People in this thread are correct in that the only thing to do is just pick one, according to your own internal logic as to whether borrowed words invite borrowed plurals. “Tori” is currently more common in the mathematical literature.
Oxford is descriptive, not prescriptive. In other words, if enough people use it wrongly, Oxford lists it.
Too many people think adding a “i” as a plural on words that sound like classical Latin sounds 'elegant".
In noting that since 2001, you have 354 posts, I feel compelled to congratulate the SDMB as a group for exercising so much restraint wrt creating threads like this.
ISTM that using “tableau” is itself a minor affectation in the first place, so, yeah, “tableaux” definitely qualifies.