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UID:DSC-22543
DTSTART;TZID=Europe/Berlin:20260108T150000
SEQUENCE:1767854230
TRANSP:OPAQUE
DTEND;TZID=Europe/Berlin:20260108T160000
URL:https://dresden-science-calendar.org/calendar/de/detail/22543
LOCATION:MPI-CBG\, Pfotenhauerstraße 10801307 Dresden
SUMMARY:Thom: On planar sections of the dodecahedron
CLASS:PUBLIC
DESCRIPTION:Speaker: Andreas Thom\nInstitute of Speaker: TU Dresden\nTopics
 :\n\n Location:\n  Name: MPI-CBG (MPI-CBG CSBD SR Top Floor (VC))\n  Stree
 t: Pfotenhauerstraße 108\n  City: 01307 Dresden\n  Phone: +49 351 210-0\n
   Fax: +49 351 210-2000\nDescription: In the analysis of three-dimensional
  biological microstructures such as organoids\, microscopy frequently yiel
 ds two-dimensional optical sections without access to their orientation. M
 otivated by the question of whether such random planar sections determine 
 the underlying three-dimensional structure\, we investigate a discrete ana
 logue in which the ambient structure is the vertex set of a Platonic solid
  and the observed data are congruence classes of planar intersections. For
  the regular dodecahedron with vertex set V\, we define the planar statist
 ic of a subset X⊆V of vertices as the distribution of isometry types of 
 inclusions Π∩X⊆Π∩V⊆V\, and ask whether this statistic determines
  X up to isometry. We show that this is not the case: there exist two non-
 isometric 7-element subsets with identical planar statistics. As a consequ
 ence\, there exist two polytopes in R3\, whose distribution of isometry cl
 asses of two-dimensional intersections is identical\, while the polytopes 
 are not themselves isometric. This result is an analogue of classical non-
 uniqueness phenomena in geometric tomography.
DTSTAMP:20260922T115130Z
CREATED:20260106T063510Z
LAST-MODIFIED:20260108T063710Z
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