Download this article
 Download this article For screen
For printing
Recent Issues
Volume 18
Volume 16
Volume 15
Volume 14
Volume 13
Volume 12
Volume 11
Volume 10
Volume 9
Volume 8
Volume 6+7
Volume 5
Volume 4
Volume 3
Volume 2
Volume 1
The Journal
About the journal
Ethics and policies
Peer-review process
 
Submission guidelines
Submission form
Editorial board
 
Subscriptions
 
ISSN (electronic): 2640-7345
ISSN (print): 2640-7337
Author Index
To Appear
 
Other MSP Journals
Vietoris–Rips complexes of platonic solids

Nada Saleh, Thomas Titz Mite and Stefan Witzel

Vol. 21 (2024), No. 1, 17–34
DOI: 10.2140/iig.2024.21.17
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.

Keywords
Vietoris–Rips complex, platonic solid, discrete Morse theory
Mathematical Subject Classification
Primary: 55N31
Secondary: 05E45, 51M20, 57Q70
Milestones
Received: 17 July 2023
Accepted: 15 January 2024
Published: 31 May 2024
Authors
Nada Saleh
Linden
Germany
Thomas Titz Mite
Mathematical Institute
Gießen University
Gießen
Germany
Stefan Witzel
Mathematical Institute
Gießen University
Gießen
Germany