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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2answers
213 views

Are there formulae to determine close-packing polyhedra?

Is there a formula to determine which polyhedra will tessellate in 3D without any spaces?
3
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1answer
169 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
2k 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 ...
2
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1answer
319 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 ...
105
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4answers
8k views

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 ...
17
votes
2answers
875 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 ...
8
votes
2answers
311 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, ...