On planar sections of the dodecahedron

Datum

08.01.2026

Zeit

15:00 - 16:00

Sprecher

Andreas Thom

Zugehörigkeit

TU Dresden

Sprache

en

Hauptthema

Biologie

Host

Local Organisers: Nikola Sadovek, Maximilian Wiesmann, Giulio Zucal

Beschreibung

In the analysis of three-dimensional biological microstructures such as organoids, microscopy frequently yields two-dimensional optical sections without access to their orientation. Motivated by the question of whether such random planar sections determine the underlying three-dimensional structure, we investigate a discrete analogue 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 statistic 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 consequence, there exist two polytopes in R3, whose distribution of isometry classes 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.

Letztmalig verändert: 08.01.2026, 07:37:10