One of the projections of the $4_{21}$ polytope (https://en.m.wikipedia.org/wiki/4_21_polytope) into four dimensions positions its vertices as those of two concentric 600-cells scaled by the golden ratio (https://vzome.com/home/geometry/gossets-polytopes/). Taking the convex hull of 120 of the $4_{21}$ corresponding to just one of these 600-cells results in a diminishing of the $4_{21}$ with 120 vertices and some number of edges. Are all these edges the same length?
$\begingroup$
$\endgroup$
3
-
3$\begingroup$ Dear Daniel. I recommend that you edit your question to include some (a lot?) of background. For example, could you please include a definition of the $4_{21}$ polytope. Also, could you please explain (sketch) why some of the facts that your cited are true? Etc. This will help other users provide useful answers to your question. $\endgroup$– André HenriquesJul 2, 2021 at 21:02
-
$\begingroup$ en.m.wikipedia.org/wiki/4_21_polytope $\endgroup$– Dima PasechnikJul 2, 2021 at 21:18
-
$\begingroup$ Wikipedia gives some relatively simple coordinates for the vertices of the $4_{21}$. Do you have an idea which of them remain after deleting half of them? Or one step further back, can you give the 4-subspace on which you project? $\endgroup$– M. WinterJul 2, 2021 at 22:13
Add a comment
|