-1
$\begingroup$

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.

Thanks for your assistance in advance.

$\endgroup$
2
  • 2
    $\begingroup$ 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. $\endgroup$
    – Toby Mak
    Sep 12, 2018 at 8:46
  • $\begingroup$ I thought of the numbers of vertices just in the base. I agree with your statement. $\endgroup$ Sep 12, 2018 at 8:55

1 Answer 1

6
$\begingroup$

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.

enter image description here

$\endgroup$
3
  • 3
    $\begingroup$ Added one such :-) $\endgroup$ Sep 12, 2018 at 10:49
  • $\begingroup$ @JyrkiLahtonen Thanks! How did you find that image? $\endgroup$
    – Toby Mak
    Sep 12, 2018 at 11:05
  • 1
    $\begingroup$ Being a tenured lecturer, I could afford to cough up the dough and purchase a personal license to Mathematica :-) It can be relatively easily coerced to produce such images. I first built a list of the coordinates and then defined a list of polygons forming this pyramid. Piece of cake, really. $\endgroup$ Sep 12, 2018 at 12:27

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.