1
vote
2answers
34 views

Is the rhombic dodecahedron the only isohedral polyhedron that tiles 3-space (other than the cube)?

Is the rhombic dodecahedron the only face-transitive (or isohedral, i.e. all faces are the same) polyhedron that seamlessly tiles 3-dimensional Euclidean space (other than the cube)? I'm looking ...
0
votes
0answers
14 views

Numerically define tessellation / tiling?

Assuming that you know how to express and define a geometric shape, either with a Cartesian coordinate system or with trigonometric curves, in a discrete set or in a complex set, there is a way to ...
1
vote
1answer
27 views

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?
5
votes
1answer
82 views

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 ...
7
votes
1answer
256 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 ...
12
votes
1answer
531 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 ...
2
votes
1answer
181 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.
12
votes
3answers
1k 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 ...
3
votes
1answer
301 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 ...
5
votes
4answers
449 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 ...