Question

Show that $S=\{\mathbf x \in \mathbb R^n:\mathbf A \mathbf x=\mathbf b,\mathbf x \ge \mathbf 0\} \ne \emptyset$ has at least one extreme point

score 739 · Answer 1 · 2026-03-29 04:34:32

739

Views

Show that $S=\{\mathbf x \in \mathbb R^n:\mathbf A \mathbf x=\mathbf b,\mathbf x \ge \mathbf 0\} \ne \emptyset$ has at least one extreme point

Published on 29 Mar 2026 - 4:34

score 98 · Answer 2 · 2021-12-08 20:45:27

98

Views

Tetrahedron from 5 edges with 3 equal lengths

Published on 08 Dec 2021 - 20:45

score 11 · Answer 3 · 2026-02-26 02:54:02

11

Views

Describe an orthoplex as a polyhedron

Published on 26 Feb 2026 - 2:54

score 173 · Answer 4 · 2026-03-27 19:32:11

173

Views

Dodecahedron and golden ratio algebra

Published on 27 Mar 2026 - 19:32

score 73 · Answer 5 · 2026-03-29 05:43:03

73

Views

Square pyramid with integer measurements.

Published on 29 Mar 2026 - 5:43

score 71 · Answer 6 · 2026-03-29 07:19:41

71

Views

Inferring dimension of a polyhedron from a point

Published on 29 Mar 2026 - 7:19

score 92 · Answer 7 · 2026-03-27 00:03:52

92

Views

Directed polyhedral graph with $d^+(v) \geq 1$ and $d^- (v) \geq 1$

Published on 27 Mar 2026 - 0:03

score 528 · Answer 8 · 2022-01-12 22:10:26

528

Views

Mapping a torus onto a sphere

Published on 12 Jan 2022 - 22:10

score 403 · Answer 9 · 2022-01-14 17:27:48

403

Views

What is the volume of the largest truncated octahedron that can be inscribed in the unit sphere?

Published on 14 Jan 2022 - 17:27

score 46 · Answer 10 · 2026-03-30 05:13:22

46

Views

Weighted volume of simplices making up a cube not equal to volume of cube?

Published on 30 Mar 2026 - 5:13

score 1k · Answer 11 · 2022-01-21 06:52:01

1k

Views

Simplicial polyhedral cones

Published on 21 Jan 2022 - 6:52

score 94 · Answer 12 · 2026-03-27 17:52:26

94

Views

How can we exclude vertices of a compact polyhedron and represent it as a convex hull?

Published on 27 Mar 2026 - 17:52

score 78 · Answer 13 · 2022-01-25 18:49:52

78

Views

Why this proof doesn't work for non convex polyhedra?

Published on 25 Jan 2022 - 18:49

score 74 · Answer 14 · 2022-01-30 22:34:55

74

Views

Finding all vertices of a polyhedron in $\Bbb{R}^n$ defined by $x_i+x_j\geq1$ and $0\leq x_i\leq 1$

Published on 30 Jan 2022 - 22:34

score 96 · Answer 15 · 2022-02-01 00:34:35

96

Views

Self-dual polyhedral and self-complementary graph

Published on 01 Feb 2022 - 0:34

List Question

Show that $S=\{\mathbf x \in \mathbb R^n:\mathbf A \mathbf x=\mathbf b,\mathbf x \ge \mathbf 0\} \ne \emptyset$ has at least one extreme point

Tetrahedron from 5 edges with 3 equal lengths

Describe an orthoplex as a polyhedron

Dodecahedron and golden ratio algebra

Square pyramid with integer measurements.

Inferring dimension of a polyhedron from a point

Directed polyhedral graph with $d^+(v) \geq 1$ and $d^- (v) \geq 1$

Mapping a torus onto a sphere

What is the volume of the largest truncated octahedron that can be inscribed in the unit sphere?

Weighted volume of simplices making up a cube not equal to volume of cube?

Simplicial polyhedral cones

How can we exclude vertices of a compact polyhedron and represent it as a convex hull?

Why this proof doesn't work for non convex polyhedra?

Finding all vertices of a polyhedron in $\Bbb{R}^n$ defined by $x_i+x_j\geq1$ and $0\leq x_i\leq 1$

Self-dual polyhedral and self-complementary graph

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