# Why can there not exist a pyramid with 29 corners?

Why can there not exist a pyramid with 29 corners?

I tried to find a pattern, it seems like I can draw a pyramids with corners, 3,4,5, and 6. 7 becomes tricky and 29 isn’t something I even can conceptualize. Ofcourse there is probably a pattern which one on the bases of would conclude that it is an impossibility.

• How can you draw a pyramid with $3$ vertices? As far as I know, you cannot have less corners than a tetrahedron, which has 4 vertices. Sep 12, 2018 at 8:46
Let the pyramids' base have $n$ vertices. There is also one more vertex on top, so there are in total $n+1$ vertices.
For a pyramid with $29$ vertices, the base must be a $28$-sided polygon. This might be hard to visualise because there are so many sides, but it is possible.