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YCor
YCor
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Constructing an $n$-Simplexsimplex at the border of a $n$-ball by orthogonal hyperplanes

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

  • Choose $n$ vectors in the boundary of an $n$ dimensional ball, which are forming an $n-1$$(n-1)$-Simplexsimplex 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$$(n-1)$-Simplexsimplex now form an $n$-Simplexsimplex?

Constructing an $n$-Simplex at the border of a $n$-ball by orthogonal hyperplanes

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?

Constructing an $n$-simplex at the border of a $n$-ball by orthogonal hyperplanes

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?

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weierstrass181
weierstrass181
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Constructing an $n$-Simplex at the border of a $n$-ball by orthogonal hyperplanes

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?