Vietoris-Rips complexes of n-by-n torus grids are shown to be tori, spheres, or wedges of spheres for several infinite families of grid sizes and scales.
Vietoris-Rips complexes of Platonic solids
1 Pith paper cite this work. Polarity classification is still indexing.
1
Pith paper citing it
abstract
We determine the homotopy type of the Vietoris-Rips complexes of the (vertex sets of the) platonic solids. The most interesting case is that the Vietoris-Rips complex of the dodecahedron is a wedge of nine 3-spheres when the parameter is between combinatorial distance 3 and 4.
citation-role summary
background 1
citation-polarity summary
fields
math.AT 1years
2025 1verdicts
CONDITIONAL 1roles
background 1polarities
background 1representative citing papers
citing papers explorer
-
Vietoris-Rips complexes of torus grids
Vietoris-Rips complexes of n-by-n torus grids are shown to be tori, spheres, or wedges of spheres for several infinite families of grid sizes and scales.