2
$\begingroup$

I want to construct an $n$-simplex the following way:

  • Choose $n$ vectors in the boundary of an $n$ dimensional ball, which are forming an $(n-1)$-simplex together.

  • Place the orthogonal affine $n-1$-hyperplane on each of these vectors.

My question now is: Does the part enclosed by these hyperplanes together with the $(n-1)$-simplex now form an $n$-simplex?

Improve this question
$\endgroup$
2
  • $\begingroup$ By "$n$-simplex" do you mean a regular $n$-simplex? $\endgroup$
    – Joseph O'Rourke
    Commented Aug 21 at 0:33
  • 1
    $\begingroup$ Yes. It comes out to the question whether those hyperplanes (given the circumstances) all intersect in one point, which becomes the $n+1$ vertex of the $n$-Simplex. $\endgroup$
    – weierstrass181
    Commented Aug 21 at 5:15

0

Reset to default

You must log in to answer this question.