Question

What are the formulas for the number of vertices, edges, faces, cells, 4-faces, ..., $n$-faces, of convex regular polytopes in $n \geq 5$ dimensions?

score 1.9k · Answer 1 · 2026-05-10 17:06:58

1.9k

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What are the formulas for the number of vertices, edges, faces, cells, 4-faces, ..., $n$-faces, of convex regular polytopes in $n \geq 5$ dimensions?

Published on 10 May 2026 - 17:06

score 248 · Answer 2 · 2026-05-10 17:06:49

248

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If we inscribed all the 6 regular convex four-dimensional polytopes in a sphere, which one would have the highest volume?

Published on 10 May 2026 - 17:06

score 794 · Answer 3 · 2026-05-10 17:06:50

794

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Why is the 24-cell (also called Icositetrachoron or Hyperdiamond) the unique regular convex polychoron which has no direct three-dimensional analog?

Published on 10 May 2026 - 17:06

score 2.6k · Answer 4 · 2026-04-12 08:01:40

2.6k

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Faces of the Permutahedron

Published on 12 Apr 2026 - 8:01

score 107 · Answer 5 · 2026-04-13 04:56:00

107

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Ehrhart polynomial of lattice tetrahedrons in $\Bbb{R}^4$

Published on 13 Apr 2026 - 4:56

score 551 · Answer 6 · 2026-04-13 11:41:50

551

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Projection onto hypercube [0,1]^n

Published on 13 Apr 2026 - 11:41

score 127 · Answer 7 · 2026-05-10 17:53:23

127

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What are the facets of the Tridiagonal Birkhoff $d$-polytope $\Omega^t_{d+1}$?

Published on 10 May 2026 - 17:53

score 49 · Answer 8 · 2026-04-11 07:38:42

49

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linear algebra question

Published on 11 Apr 2026 - 7:38

score 77 · Answer 9 · 2026-04-13 23:53:27

77

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Discrete Analogue of the Poincaré Conjecture and Simple Connectedness

Published on 13 Apr 2026 - 23:53

score 91 · Answer 10 · 2026-04-11 20:11:56

91

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dimension of Weber set and selectope (as a operator)

Published on 11 Apr 2026 - 20:11

score 124 · Answer 11 · 2026-05-10 16:12:41

124

Views

Count and description of vertices of certain faces - called MTBFs - of the Tridiagonal Birkhoff polytope $\Omega^t_{d+k}$

Published on 10 May 2026 - 16:12

score 90 · Answer 12 · 2026-04-16 05:15:42

90

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On the Name of the Amplituhedron

Published on 16 Apr 2026 - 5:15

score 697 · Answer 13 · 2026-04-15 06:23:47

697

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Proof: Minkowski sum polytope implies A and B polytopes

Published on 15 Apr 2026 - 6:23

score 59 · Answer 14 · 2026-05-10 22:02:38

59

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How to show that the vertices of a convex hull are given by these specific subsets...

Published on 10 May 2026 - 22:02

score 66 · Answer 15 · 2026-04-15 17:05:27

66

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Number of Half-Unit Pentachora in a Unit Hexacosichoron

Published on 15 Apr 2026 - 17:05

List Question

What are the formulas for the number of vertices, edges, faces, cells, 4-faces, ..., $n$-faces, of convex regular polytopes in $n \geq 5$ dimensions?

If we inscribed all the 6 regular convex four-dimensional polytopes in a sphere, which one would have the highest volume?

Why is the 24-cell (also called Icositetrachoron or Hyperdiamond) the unique regular convex polychoron which has no direct three-dimensional analog?

Faces of the Permutahedron

Ehrhart polynomial of lattice tetrahedrons in $\Bbb{R}^4$

Projection onto hypercube [0,1]^n

What are the facets of the Tridiagonal Birkhoff $d$-polytope $\Omega^t_{d+1}$?

linear algebra question

Discrete Analogue of the Poincaré Conjecture and Simple Connectedness

dimension of Weber set and selectope (as a operator)

Count and description of vertices of certain faces - called MTBFs - of the Tridiagonal Birkhoff polytope $\Omega^t_{d+k}$

On the Name of the Amplituhedron

Proof: Minkowski sum polytope implies A and B polytopes

How to show that the vertices of a convex hull are given by these specific subsets...

Number of Half-Unit Pentachora in a Unit Hexacosichoron

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