How to Build a Teepee - Part One

I am building an indoor teepee.

Don't ask why, come over and see it!

Well anyhow, how do you build a teepee?

I seem to remember the one-off fieldtrip to the bush in grade 6 or 7 when my elementary school went on Indian sensitivity training. Or if you prefer First Nations cultural learning day. Too bad we only got to go the once in my entire educational career. Anyhow, Mrs. Beaverbone showed our group how to put up a teepee. It had 4 poles I think, one for each direction, 4 more, to hold the skin more round-like and two to hold open the smoke hole.

Now, how do I reckon how much covering I should use? Apparently, the surface area of a cone can be expressed as (1/2)(s)(C) where "s" is the slant height and "C" is the circumference of the circular base. Anyhow, I had the geometry figured on scrap paper on my lunch at Home D.

To double check, I went to Mr. Google. It makes sense, circumference times height=cylinder surface. Divide it in half you have a cone. Ok, I just had to reason it in my mind.

Now, on the other hand, what about the smoke hole? Should I make the overall shape more cylindrical? Chop the top of the cone off? I think so, I have to accomodate twelve bamboo sticks lashed together.

The material is a painter's drop cloth obtained from Home D... sadly. My original intention was to use felt, about 1/4 inch thick. But I figured it would cost too much. No research went into this assumption. So anyone with info can berate my unscientific conclusion here.

Armed with my trusty Corsican penknife, je coupe la ficelle that holds the bamboo in a bundle.
There's a brilliant essay on the comfort of having a penknife in your pocket, in French, by Phillipe Delerm. I wonder if it's translated?

Some quick boy scout lashing later, and the basic tripod is set. I discovered that bamboo slides a lot on hardwood flooring, I may need to make the "feet" of my poles sticky somehow (pieces of punctured bike tubes?)
Covering a rectangular bed with a round structure is not the simplest task. I think I'll get some foam and cut my own mattress after I get paid...