Question

The Schläfli Symbol for tilings of regular polygons with irregular tiles

score 104 · Answer 1 · 2026-03-25 12:27:06

104

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The Schläfli Symbol for tilings of regular polygons with irregular tiles

Published on 25 Mar 2026 - 12:27

score 76 · Answer 2 · 2023-09-17 16:52:19

76

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There two types of tiles, we need to construct a $2 \times n$ rectangle filled with them. How many ways are there to do that?

Published on 17 Sep 2023 - 16:52

score 88 · Answer 3 · 2026-03-26 19:05:20

88

Views

What tools can show that (possibly irregular) dodecahedra do not fill space?

Published on 26 Mar 2026 - 19:05

score 33 · Answer 4 · 2023-09-23 13:07:04

33

Views

Is Kelvin structure the optimal solution for a three-dimensional foam when restricted to only one shape?

Published on 23 Sep 2023 - 13:07

score 29 · Answer 5 · 2023-10-01 14:48:14

29

Views

Are all convex hexagonal space tilings either double lattices or triple lattices?

Published on 01 Oct 2023 - 14:48

score 175 · Answer 6 · 2023-10-02 20:58:01

175

Views

What regular polyhedra can be tightly packed?

Published on 02 Oct 2023 - 20:58

score 72 · Answer 7 · 2023-10-03 12:58:53

72

Views

Why aren't $59$ L tiles the answer to this problem?

Published on 03 Oct 2023 - 12:58

score 729 · Answer 8 · 2026-02-23 02:42:07

729

Views

Union of two disjoint congruent polygons is centrally symmetric. Must the polygons differ by a 180 degree rotation?

Published on 23 Feb 2026 - 2:42

score 69 · Answer 9 · 2023-10-20 02:18:31

69

Views

One X-pentomino and any number of I-trominoes cannot tile a rectangle?

Published on 20 Oct 2023 - 2:18

score 108 · Answer 10 · 2023-10-21 18:33:58

108

Views

Reinhardt's Polyhedron as the first couterexample to the second part of Hilbert's 18th problem

Published on 21 Oct 2023 - 18:33

score 3.4k · Answer 11 · 2023-10-22 00:08:41

3.4k

Views

Is it possible to assemble copies of this shape into a cube?

Published on 22 Oct 2023 - 0:08

score 84 · Answer 12 · 2023-10-25 19:08:21

84

Views

Wiping a plane clean with a rectangle (chalkboard erasing alogrithm?)

Published on 25 Oct 2023 - 19:08

score 79 · Answer 13 · 2026-03-26 16:05:04

79

Views

The 18 golden rational tetrahedra

Published on 26 Mar 2026 - 16:05

score 140 · Answer 14 · 2026-02-23 04:47:12

140

Views

How many domino tilings of a $2n\times 2n$ board are uniquely 3-colourable?

Published on 23 Feb 2026 - 4:47

score 127 · Answer 15 · 2026-02-23 04:49:47

127

Views

Coloring a polyomino tiling so that no two pieces with the same color have a common point

Published on 23 Feb 2026 - 4:49

List Question

The Schläfli Symbol for tilings of regular polygons with irregular tiles

There two types of tiles, we need to construct a $2 \times n$ rectangle filled with them. How many ways are there to do that?

What tools can show that (possibly irregular) dodecahedra do not fill space?

Is Kelvin structure the optimal solution for a three-dimensional foam when restricted to only one shape?

Are all convex hexagonal space tilings either double lattices or triple lattices?

What regular polyhedra can be tightly packed?

Why aren't $59$ L tiles the answer to this problem?

Union of two disjoint congruent polygons is centrally symmetric. Must the polygons differ by a 180 degree rotation?

One X-pentomino and any number of I-trominoes cannot tile a rectangle?

Reinhardt's Polyhedron as the first couterexample to the second part of Hilbert's 18th problem

Is it possible to assemble copies of this shape into a cube?

Wiping a plane clean with a rectangle (chalkboard erasing alogrithm?)

The 18 golden rational tetrahedra

How many domino tilings of a $2n\times 2n$ board are uniquely 3-colourable?

Coloring a polyomino tiling so that no two pieces with the same color have a common point

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