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Daniel Sebald
Daniel Sebald
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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?

One of the projections of the $4_{21}$ polytope into four dimensions positions its vertices as those of two concentric 600-cells scaled by the golden ratio. 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?

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?

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Daniel Sebald
Daniel Sebald
  • 2.8k
  • 6
  • 19

Diminishing of the $4_{21}$

One of the projections of the $4_{21}$ polytope into four dimensions positions its vertices as those of two concentric 600-cells scaled by the golden ratio. 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?