Tagged Questions

Use this tag for questions about (not necessarily periodic) tilings of metric spaces, their combinatorial, topological and dynamical properties, as well as basic definitions and concepts.

30 views

Coverings of a rectangle

How many coverings of the rectangle with height $1$ and length $n$ exist, if we use only tiles with height $1$ of the following 6 types: The solution should be in a closed form (formula).
22 views

Wallpaper groups

I am trying to understand the wallpaper groups and their symmetries. For example consider the following tiling : I believe that the symmetries are two translations, a $120^\circ$-rotation and a ...
1k views

Why a tesselation of the plane by a convex polygon of 7 or more sides is not possible?

I read in several places, including Wikipedia, that a tessellation of the plane by a single, convex, $n-$sided polygon is not possible for $n\geq7$. I was not able to locate a proof, or a paper that ...
4k views

Tiling pentominoes into a 5x5x5 cube

I have this wooden puzzle composed of 25 y-shaped pentominoes, where the objective is to assemble them into a 5x5x5 cube. After spending quite a few hours unsuccessfully trying to solve the puzzle, I ...
50 views

Plane tesselation, using stairs $n\times n$, is it possible?

The other day I was constructing new mathematical problems for my pupils and thought of something like this: Given the infinite sequence of "stairs" $n\times n$, constructed from $1\times1$ ...
63 views

Aperiodic tessellations of the plane

Here are some examples of non-periodic tessellations of the plane. Sir Roger Penrose is the expert in that field. How could someone go about proving that a certain tiling of the infinite plane with ...
2k views

249 views

Squaring the plane, with consecutive integer squares. And a related arrangement

Q1. I was fiddling around with squaring-the-square type algebraic maths, and came up with a family of arrangements of $n^2$ squares, with sides $1, 2, 3\ldots n^2$ ($n$ odd). Which seems like it would ...
194 views

Generating function for number of different tessellation checkered rectangle

Let $R_n$ be checkered rectangle sized $n \times 4, n \ge 1$. Let $a_n$ be number of different $R_n$ tiling with rectangles sized $1 \times 3$. $\ \ \$ $\ \ \$ $\ \ \$ $\ \ \$ $\ \ \$ $\ \ \$...
111 views

27 views

Tiling the concave polygons with non-polygons

Suppose that we reside in the set of all concave polygons (that is, polygons which are non-convex and simple, simple means that the boundary of the polygon does not cross itself). Let us denote that ...
40 views

Equilateral polygon plane tiling

From playing around with some toothpicks and peas, I think that it should be possible to prove that the plane cannot be tiled by a possibly infinite set of equilateral polygons with the same number of ...