I've got five cardinals, one without its mate.
My house is made of exactly four-hundred and thirty-five nice solid bricks.
(I'm kidding - they're rather fluffy.)
My length is about two hundred and forty-three, give or take.
My bench has nine legs - really, no tricks!
Mathematically, I have some interesting attributes, too:
a hyperbolic trig function in my middle, a quadratic on my left,
and - once a year - a sphere on my right. Yoo-hoo!
My whole is, in a way, a complicated plane shape who from 2D has left.
Note: just for fun, I made a question with the knowledge and trivia tags - see here for why.
Note: I replaced "chair" with "bench". I think it's a little more accurate this way.
The specific trig function is the hyperbolic cosine function. It has a very famous application. That application is what that line's clue is driving at.
The sphere exists every 365 days (366 every four years, of course), and is used to celebrate a certain event that happens with that regularity. It is destroyed at the end (or beginning?) of the event.