#Polytopes

Alexander Kasprzyk

@amkasprzyk.bsky.social

2 months ago

Positive Polytopes with Few Facets in the Grassmannian In this article we study adjoint hypersurfaces of geometric objects obtained by intersecting simple polytopes with few facets in P^5 with the Grassmannian Gr(2,4). These generalize the positive Grassmannian, which is the intersection of Gr(2,4) with the simplex. We show that if the resulting object has five facets, it is a positive geometry and the adjoint hypersurface is unique. For the case of six facets we show that the adjoint hypersurface is not necessarily unique and give an upper bound on the dimension of the family of adjoints. We illustrate our results with a range of examples. In particular, we show that even if the adjoint is not unique, a positive hexahedron can still be a positive geometry.

"Positive Polytopes with Few Facets in the Grassmannian" by Dmitrii Pavlova and Kristian Ranestad. #ExperimentalMath #AlgebraicGeometry #Polytopes

quinnnen (comms no)

@quinnenisstupid.bsky.social

2 months ago

there's this thing i want to make called diminish. basically n-dimensional minecraft where you choose the n (or use point-and-click mode to play all n at once) that would be cool i think #minecraft #polytopes

Jonny

@jonny.z-space.ca

1 year ago

YIL (yesterday I learned) Alicia Boole Stott, daughter of George Boole (of Boolean alegbra) - painted 4D shapes with water color and introduced the word 'polytope': a convex solid in 4 or more dimensions. So cool. lostprofile.tumblr.com/post/1890891... #math #polytopes
via @milanks.com as usual

André Ourednik

@andre-ourednik.bsky.social

1 year ago

Alicia #Boole au pays des #polytopes :

Au départ, il y a les cinq « solides platoniciens » vénérés en géométrie depuis l'Antiquité : le cube, le tétraèdre, l’octaèdre, le dodécaèdre et l’icosaèdre. Mais pourquoi s’arrêter aux 3 dimensions de l’espace ordinaire ? Alicia Boole Stott a consacré sa

Matthias Köppe

@mkoeppe.bsky.social

5 years ago

Do you like your #polytopes 🧊 geometric or combinatorial? Rational or irrational? @sagemath has them all, say J-P Labbé and Jonathan Kliem @FU_Berlin at the Global Virtual SageDays 109: a 50-hour around-the-clock meeting starting Wednesday https://wiki.sagemath.org/days109 #OpenSource