The comparison with a 12 dimensional shape is inadequate. We can describe a 12 dimensional object without contradiction. One might have difficulty imagining such a thing physically, but it's properties are knowable. By contrast, a square triangle, or for a simpler example a married bachelor is a contradiction. It boils down to something being both true and not true at the same time. And if we can claim that something can be both true and not true at once, then we can make absurd claims like God is both omnipotent and not.
EDIT:
You're also misunderstanding what a mathematical axiom is. Axioms are arbitrary premises that are declared to be true, but aren't true in any objective way. Mathematics does not study nature, it studies hypotheticals that sometimes behave analogously to nature. Triangles or numbers, don't exist in the same sense as physical things. There are no triangles, much less square triangles, around us, except in so far as there are things that are very similar to triangles. Now sure you could call a particular triangle like thing in nature a triangle, but that would be a different definition. And if it's found that the triangle in nature had a particular property, it's not automatically true that mathematical triangles have the same property. For example, the Bermuda Triangle, being on the surface of a the earth, does not have angles that add up to 180 degrees, but that does not allow us to say that euclidean geometry is wrong.
What I'm saying about square triangles doesn't depend on Mathematical axioms being "abstract", "hypothetical" or otherwise "not-real"; I'm just describing something that appears contradictory (i.e. a square triangle; an object that is both 3-sided and 4-sided simultaneously). Separately, that a 12-dimensional object is logically consistent is again irrelevant to the separate point I was making about my inability to imagine a 12-dimensional object; I'm merely describing something that I can't imagine.
To be clear, I am not in any way comparing a 12 dimensional object to a square triangle or a married bachelor. I am saying that (a) a square triangle / married bachelor contradicts my logical intuitions, and (b) a 12 dimensional object is beyond my comprehension. The purpose of (a) is to pose the following questions: What if some, most or all of my logical intuitions are wrong? What if logically contradictory things
can exist? The purpose of (b) is to pre-empt the response: "well, how could that possibly be? I can't imagine how a man can be both married and unmarried at the same time, or how an omnipotent being can create a rock that even he can't lift." So what if you can't imagine it? I can't imagine a 12 dimensional object, but that can still exist (it's logically consistent, after all!).
Why is it absurd to claim that something can be both true and false at the same time? I mean, I know why it's absurd for normal people to claim that, in the real world, in every day life, because we wouldn't get anywhere without logical consistency and analytical rigour. But just because the claim isn't very useful doesn't mean it can't be true. I think it can be true that God can create an object that even he can't lift -- and, simultaneously, that he can lift it because he is omnipotent. You ever had a dream where you were your adult self, at 27 years old or whatever, but were still in school, aged 7, standing in front of the entire year without pants on? Doesn't make any sense that you are your 27 year old present self but also simultaneously your 7 year old past self, but you knew that both things were true. In your head, both things were true, and you just accepted it as a fact along with everybody else. You just accept that, oh, I'm 27 and I need to get up for work in the morning, but also I'm 7 and I forgot to put my pants on for some reason and now my schoolfellows are laughing at me. Why can't the universe be like that? At least some of the time, anyway. I don't think any that
is true, and I don't think it's useful to believe it's true either, but I think it's useful to believe that it could be true.