Timeline for Can I build infinitely many polytopes from only finitely many prescribed facets?
Current License: CC BY-SA 4.0
4 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Jan 29, 2020 at 12:08 | vote | accept | M. Winter | ||
| Jan 27, 2020 at 17:30 | comment | added | Dmitri Panov | Yes, spherical polytopes are subsets in $\mathbb S^n$ bounded by geodesic $n-1$-spheres. To each vertex $p$ of an Euclidean polytope $P $ in $\mathbb R^n$ we associate a spherical polytope in $\mathbb S^{n-1}$: take a small radius $r$ sphere $S_r^{n-1}$ in $\mathbb R^n$ centred at $p$ and take the intersection $S_r^{n-1}\cap P$. This is the spherical polytope, just scale it by $1/r$ so that it lies in $\mathbb S^{n-1}$ (i.e. in a sphere of radius $1$). | |
| Jan 27, 2020 at 17:06 | comment | added | M. Winter | Thank your for your answer! I need to better understand your definitions: why do you explicitly speak of spherical polytopes, and why are they subsets of $\Bbb S^n$ and not $\Bbb R^n$? | |
| Jan 27, 2020 at 15:08 | history | answered | Dmitri Panov | CC BY-SA 4.0 |