For question on Tessellations, the process of creating a two-dimensional plane using the repetition of a geometric shape with no overlaps and no gaps.

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What is the dual lattice of Kagome lattice?

We know that the dual lattice of a triangular lattice is the honeycomb lattice. What is the dual lattice of Kagome lattice?
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Covering an area equally with layers of non-tesselating polygons

A series of hexagons on an hexagonal lattice means that the every point in the entire area is covered by one polygon only. A grid of octagons will not tesselate, leaving square holes such that 4/18 ...
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Simulation of typical cell in Poisson Voronoi tessellation

I would like to simulate a typical cell in Poisson-Voronoi tessellation model. I want to save the Cartesian coordinates of all vertices of the typical cell for each realization. How to do it? Thank ...
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From Icosahedron to Pentagonal hexecontahedron (Floret Tessellation)

Inspired by this post: Floret Tessellation of a Sphere I tried to transform myself an icosahedron into its simplest Floret tessellation. But I am having trouble when applying the 'method' given in the ...
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The maths behind 'Sky and Water 1' by Escher

I've been inspired by Eschers 'Sky and Water1' woodcut, his work is so mindblowing, it got me thinking whats the maths behind it. How did he do it?
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Plane tessellation $6^2*3^2$

An article I am reading mentioned "the plane tessellation $6^2*3^2$", I tried looking it up and I found all sort of plane tessellations - but not $6^2*3^2$. However, I did find information about ...
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How to find the center of of rotational symmetry in a Penrose tiling?

The center of Helsinki sports a gorgeous Penrose tiled pavement: Could anybody give me an algorithm that will permit me to find its 'center' - that is, the point around which the five-fold ...
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Proof that 12 in a row tic-tac-toe is a tie game?

How can be it proved that tic-tac-toe on an infinite grid (winning with 12 in a row, a column or a diagonal) can always end in a tie (with optimal strategies of both players)? There is a hint: to use ...
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Which functions preserve convexity of the cells of a polyhedral tessellation of $\mathbb{R}^n$?

Let $\mathcal{X}_1, \ldots, \mathcal{X}_m \subseteq \mathbb{R}^n$ be disjoint sets with $\bigcup_{i=1}^m \mathcal{X}_i = \mathbb{R}^n$. Furthermore, let each $\mathcal{X}_i$, $i = 1, \ldots, m$, be an ...
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Regular polygon tessellation

A roof if made up of regular tiles, much like a chessboard. The tiles overlap at the base and cannot be the same colour as the ones either to the left, right, up or down to tile. If another colour ...
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Does there exist a tessellation of a 3-D object such that no two objects touch by corner or edge only?

A hex grid is special in 2D geometry because it can tile itself in a way such that any two hexagons that touch a corner must also touch by an edge. This makes it useful for game planning because the ...
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what is the theoretical solution to Voronoi domain distribution for 2D random point sets

Consider a large set of random points in 2D plane generated by Poisson process. And consider only the finite Voronoi domains generated using these points. Is there a theoretical solution to the ...