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SUMMARY:Visualizing the higher dimensions: the regular polytopes in four d
 imensions and higher [Toeplitz Colloquium]
DTSTART:20260427T140000Z
DTEND:20260427T160000Z
DTSTAMP:20260719T032100Z
UID:indico-event-1196@math-events.uni-bonn.de
DESCRIPTION:Speakers: Paulo Freire (Max-Planck-Institut für Radioastronom
 ie Bonn)\n\nAbstract\nIn this talk\, I will present some projections of hi
 gher-dimensional polytopes to our 3-D space. This includes especially the 
 four-dimensional regular polytopes\, but I will also present some addition
 al six-dimensional and one eight-dimensional polytope. I start the talk by
  making a brief presentation of the Zometool system. This will be followed
  by a discussion of some of the different types of projections\, with an e
 mphasis on orthographic projections\, highlighting the fact that they are 
 affine transformations\, and what this implies for the projections. I then
  continue discussing the properties of the Platonic solids and their proje
 ctions to two dimensions\, especially their symmetries and how the symmetr
 y of the polyhedron is related to the symmetry of the projection. I will a
 lso discuss how the symmetries affect directly the geometric properties of
  polyhedra and their projection. I then introduce the four-dimension analo
 gues of the Platonic solids\, the regular polychora\, with a discussion of
  some of their projections to three-dimensional space represented by Zomet
 ool models\, with a detailed discussion of their symmetries and the symmet
 ries of their projections. At this stage\, the audience will be able to pa
 rticipate in the construction of a model of one of the regular polychora\,
  the Icosahedral projection of the 600-cell. Finally\, I will mention some
  interesting objects in higher dimensions\, and some general principles fo
 r constructing their projections.\n\nhttps://math-events.uni-bonn.de/event
 /1196/
LOCATION:Endenicher Allee 60/1-016 - Lipschitzsaal (Mathezentrum)
URL:https://math-events.uni-bonn.de/event/1196/
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