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 · 2026-03-25 03:04:14

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 25 Mar 2026 - 3:04

score 247 · Answer 2 · 2026-03-25 03:04:05

247

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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 25 Mar 2026 - 3:04

score 793 · Answer 3 · 2026-03-25 03:03:15

793

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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 25 Mar 2026 - 3:03

score 2.6k · Answer 4 · 2014-07-09 16:59:09

2.6k

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Faces of the Permutahedron

Published on 09 Jul 2014 - 16:59

score 105 · Answer 5 · 2026-03-25 16:03:06

105

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

Published on 25 Mar 2026 - 16:03

score 548 · Answer 6 · 2014-09-13 07:58:22

548

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Projection onto hypercube [0,1]^n

Published on 13 Sep 2014 - 7:58

score 123 · Answer 7 · 2026-03-22 19:12:15

123

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

Published on 22 Mar 2026 - 19:12

score 46 · Answer 8 · 2014-09-18 14:15:33

46

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linear algebra question

Published on 18 Sep 2014 - 14:15

score 74 · Answer 9 · 2014-09-27 23:37:13

74

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Discrete Analogue of the Poincaré Conjecture and Simple Connectedness

Published on 27 Sep 2014 - 23:37

score 88 · Answer 10 · 2014-10-08 08:58:53

88

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dimension of Weber set and selectope (as a operator)

Published on 08 Oct 2014 - 8:58

score 119 · Answer 11 · 2026-03-23 10:50:10

119

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

Published on 23 Mar 2026 - 10:50

score 87 · Answer 12 · 2014-10-16 17:05:56

87

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On the Name of the Amplituhedron

Published on 16 Oct 2014 - 17:05

score 694 · Answer 13 · 2014-10-22 06:28:18

694

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Proof: Minkowski sum polytope implies A and B polytopes

Published on 22 Oct 2014 - 6:28

score 56 · Answer 14 · 2026-03-25 16:03:35

56

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

Published on 25 Mar 2026 - 16:03

score 63 · Answer 15 · 2014-10-23 18:09:44

63

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Number of Half-Unit Pentachora in a Unit Hexacosichoron

Published on 23 Oct 2014 - 18:09

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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