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Results tagged with convex-polytopes
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user 10235
Convex polytopes are the convex hulls of a finite set of points in Euclidean spaces. They have rich combinatorial, arithmetic, and metrical theory, and are related to toric varieties and to linear programming
2
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1
answer
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Definition of "regular" in Stringham's "Regular figures in n-dimensional space"
I've been reading Irving Stringham's 1880 thesis, "Regular Figures in n-dimensional Space" (only 14 pages!), after it was mentioned by Coxeter in Regular Polytopes (§7.x).
I'm confused about what Stri …
- 590
8
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Vertex-transitive polytopes in any dimension with any number of vertices?
For any even $d$, and any $v \geq d + 1$, the answer is yes; take the cyclic polytope $C_d(v)$, consisting of $v$ points on the moment curve $(t, t^2, \dotsc, t^d)$. Any choice of points gives a combi …
- 590
4
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Is there any edge- but not vertex-transitive polytope in $d\ge 4$ dimensions?
If you consider a tiling of 3-space to be a 4-dimensional polytope, then the Rhombic dodecahedral honeycomb would work.
Other possibilities are limited by the potential 3-faces.
Because every edge h …
- 590