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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Giant Pufferfish skin pattern―how could that be generated
I just started my investigations about tesselations and tilings for some very special kind of design Project. I came over that image:
It shows a part of the Giant Pufferfish's skin and I am very ...
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3answers
101 views
Why are triangles, squares and hexagons the only polygons with which it is possible to tile a plane?
Ok so I have heard that the only regular polygons which can completely fll the plane without overlaping are the 3,4 and 6 sided ones. I have also heard about penrose tilings but this question ignores ...
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1answer
41 views
Mathematical notation to describe tiling shapes?
I stumbled across the following Wikipedia article which contained information on tiling by regular polygons.
Underneath each image, it contained a sort of sequence of numbers which appears to be ...
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52 views
How to draw a regular tessellation of a sphere on a plane?
I have really been stuck with this for a while. Any help will be much appreciated --
Is there a nice way to draw a tessellation of a sphere, say where three 4-polygons meet at every vertex, on a ...
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3answers
80 views
Dissecting an equilateral triangle into equilateral triangles of pairwise different sizes
It is know that a square can be dissected into other square such that no two of the squares have the same size.
This is the simplest dissection of that kind:
Is it also possible to dissect an ...
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28 views
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 ...
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1answer
131 views
What tesselated three-dimensional shape gives the maximum volume with the minimum surface area?
I recently read an article on the future of buildings. I have long been interested in architecture and it seems to me that this article makes some very good points. It got me thinking about 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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1answer
156 views
How is tessellation defined in Mathematics?
Hi. I am a GCSE student and I am interested in Maths.
I read few books on maths and learned some mathematical analysis.
I know of convergent series but I would like to know how identical sets(not ...
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1answer
286 views
Floret Tessellation of a Sphere
I'm a programmer looking to create a 3D model of a Floret Tessellation of a sphere, like the one in this picture
Class III 8,11 floret planar net
(source)
If anyone could point me in the right ...
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votes
1answer
116 views
Aperiodic hexagonal tiling?
Is there any known aperiodic tiling of the plane using hexagons?
Wang tiles are a known aperiodic tiling using squares. I'm looking for something similar using hexagons.
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28 views
Largest online database of quasicrystal
This paper gives a broken link and Google was not of any help either yielding introductory materials on the subject. Anyone knows if the database (if it exists) has been moved to a new server and if ...
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558 views
how to generate tesselation cells using the Poincare disk model?
I'm a computer programmer, and while I like math, this is an area where my understanding of math falls short of what I need in order to apply it successfully.
I've been looking at M.C. Escher's ...
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0answers
58 views
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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1answer
167 views
A Voronoi diagram with two dimensional generators on a “warped” plane
Consider this set of two dimensional generators (red polygons top left). A Voronoi diagram of these polygons is shown at bottom left. Now consider the same set of two dimensional generators on some ...
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1answer
215 views
Is there a way to tessellate an area using triangles and minimize/specify the number of unique triangles?
Is it possible to tessellate a planar surface from triangles but with the following constraints:
density (average number of triangles) can be varied.
a finite set of unique triangles are used for ...
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vote
1answer
91 views
How do I calculate the unique k-dimensional hypersphere's center from k+1 points?
I'm working with the Bowyer-Watson algorithm to determine the Delaunay tessellation of stochastic points in k-dimensional space. This algorithm assumes that the center of a simplex can be used as the ...
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1answer
101 views
counting edges in tesselations of a torus
Tesselate a torus with finitely many simply connected polygons. Do not allow four or more of them to meet at a point. In counting the edges, don't count a "straight line" as just one edge if it's ...
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4answers
288 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 ...
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1answer
134 views
Are there formulae to determine close-packing polyhedra?
Is there a formula to determine which polyhedra will tessellate in 3D without any spaces?
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1answer
93 views
Triangulation on Euclidean Space
I have a couple of questions about triangulations of the Euclidean space:
Is it possible to have an infinite triangulation of the Euclidean space $\mathbb{R}^2$ such that only a finite number of ...
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2answers
504 views
Employing optimal packing, how many circles (51 mm diameter) can I cut from a rectangle (330 mm×530 mm)
I know that I should use some kind of honeycomb structure but can't work out in which orientation I should arrange it. I've looked at a few websites now and although I have a slightly better idea of ...
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1answer
194 views
Rotation of Tetrehedra for 3d Tessellation
I'm trying to render some 3d graphics with a bunch of tetrahedra. I'm trying to figure out how to rotate one tetrahedron such that it will be perfectly face-to-face with another tetrahedron. If this ...
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3answers
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Can someone explain the math behind tessellation?
Tessellation is fascinating to me, and I've always been amazed by the drawings of M.C.Escher, particularly interesting to me, is how he would've gone about calculating tessellating shapes.
In my ...
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2answers
467 views
doubly periodic functions as tessellations (other than parallelograms)
I think of a snapshot of a single period of a doubly periodic function as one parallelogram-shaped tile in a tessellation, could a function have a period that repeats like honeycomb or some other not ...
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2answers
157 views
What is the most frequent number of edges of Voronoi cells of a large set of random points?
Consider a large set of points with coordinates that are uniformly distributed within a unit-length segment. Consider a Voronoi diagram built on these points. If we consider only non-infinite cells, ...
