Question

A convex polyhedron has 20 vertices and 12 faces. Each face of the polyhedron is bounded by the same number of edges. What is this common number?

score 333 · Answer 1 · 2026-03-25 09:51:17

333

Views

A convex polyhedron has 20 vertices and 12 faces. Each face of the polyhedron is bounded by the same number of edges. What is this common number?

Published on 25 Mar 2026 - 9:51

score 405 · Answer 2 · 2026-03-26 04:53:41

405

Views

Is there a conformal mapping from the surface of a cube to the surface of a spherical cube that preserves edges?

Published on 26 Mar 2026 - 4:53

score 308 · Answer 3 · 2026-03-26 06:23:10

308

Views

What is the name of the shape generated by the vertices of the Soviet pennant on the Luna 2 spacecraft? Is it an polyhedron?

Published on 26 Mar 2026 - 6:23

score 291 · Answer 4 · 2026-03-25 22:06:22

291

Views

How to understand the Conway recipe C969qD to construct this polyhedron? Canonicalization then quinto?

Published on 25 Mar 2026 - 22:06

score 380 · Answer 5 · 2019-03-26 22:43:53

380

Views

Why are there only 13 Archimedean solids and not 14?

Published on 26 Mar 2019 - 22:43

score 281 · Answer 6 · 2019-03-28 05:55:05

281

Views

What are all possible orientations of the Platonic Solids?

Published on 28 Mar 2019 - 5:55

score 352 · Answer 7 · 2026-03-25 04:40:30

352

Views

Neighboring solids in tetrahedral-octahedral honeycomb

Published on 25 Mar 2026 - 4:40

score 2.7k · Answer 8 · 2026-03-25 03:22:49

2.7k

Views

How is a nonnegative orthant a cone?

Published on 25 Mar 2026 - 3:22

score 130 · Answer 9 · 2019-04-08 02:20:01

130

Views

What physical features of the tetrahedron prevent its symmetry group from being all of $S_4$?

Published on 08 Apr 2019 - 2:20

score 466 · Answer 10 · 2026-03-26 06:10:34

466

Views

Euler's Formula To Show 2E=3V

Published on 26 Mar 2026 - 6:10

score 327 · Answer 11 · 2019-04-08 22:58:00

327

Views

Distribution of points on a sphere

Published on 08 Apr 2019 - 22:58

score 78 · Answer 12 · 2019-04-09 11:49:44

78

Views

Area of Convex polyhedron (2D) with unordered vertices

Published on 09 Apr 2019 - 11:49

score 31 · Answer 13 · 2026-03-25 07:38:21

31

Views

Construct Polytopes from Arbitrary Edge Sets

Published on 25 Mar 2026 - 7:38

score 61 · Answer 14 · 2026-03-25 12:12:17

61

Views

Linear program geometry

Published on 25 Mar 2026 - 12:12

score 41 · Answer 15 · 2019-04-14 21:37:12

41

Views

What solid does the truncation of an icosahedron approach?

Published on 14 Apr 2019 - 21:37

List Question

A convex polyhedron has 20 vertices and 12 faces. Each face of the polyhedron is bounded by the same number of edges. What is this common number?

Is there a conformal mapping from the surface of a cube to the surface of a spherical cube that preserves edges?

What is the name of the shape generated by the vertices of the Soviet pennant on the Luna 2 spacecraft? Is it an polyhedron?

How to understand the Conway recipe C969qD to construct this polyhedron? Canonicalization then quinto?

Why are there only 13 Archimedean solids and not 14?

What are all possible orientations of the Platonic Solids?

Neighboring solids in tetrahedral-octahedral honeycomb

How is a nonnegative orthant a cone?

What physical features of the tetrahedron prevent its symmetry group from being all of $S_4$?

Euler's Formula To Show 2E=3V

Distribution of points on a sphere

Area of Convex polyhedron (2D) with unordered vertices

Construct Polytopes from Arbitrary Edge Sets

Linear program geometry

What solid does the truncation of an icosahedron approach?

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