Search results
Results from the WOW.Com Content Network
If a geometric shape can be used as a prototile to create a tessellation, the shape is said to tessellate or to tile the plane. The Conway criterion is a sufficient, but not necessary, set of rules for deciding whether a given shape tiles the plane periodically without reflections: some tiles fail the criterion, but still tile the plane. [19]
Infinitely many different pentagons can form this pattern, belonging to two of the 15 families of convex pentagons that can tile the plane. Their tilings have varying symmetries; all are face-symmetric. One particular form of the tiling, dual to the snub square tiling, has tiles with the minimum possible perimeter among all pentagonal tilings ...
In plane geometry, the einstein problem asks about the existence of a single prototile that by itself forms an aperiodic set of prototiles; that is, a shape that can tessellate space but only in a nonperiodic way. Such a shape is called an einstein, a word play on ein Stein, German for "one stone". [2]
The honeycomb conjecture states that hexagonal tiling is the best way to divide a surface into regions of equal area with the least total perimeter. The optimal three-dimensional structure for making honeycomb (or rather, soap bubbles) was investigated by Lord Kelvin , who believed that the Kelvin structure (or body-centered cubic lattice) is ...
By extension of this relation, a plane can be tessellated by a single pentagonal prototile shape in ways that generate hexagonal overlays. For example: Planar tessellation by a single pentagonal prototile (type 1) with overlays of regular hexagons (each comprising 2 pentagons).
The origin of this type of tessellated pavement remains uncertain. The size and shape of these polygons appears to be dependent to a large extent on the grain size, texture, and coherence of the rock. This polygonal tessellation is best developed in relatively fine-grained, uniform, and siliceous or silicified sandstones. [1]
Such a shape necessarily forms the prototile for a tiling of the plane, in many cases an aperiodic tiling. A rep-tile dissection using different sizes of the original shape is called an irregular rep-tile or irreptile. If the dissection uses n copies, the shape is said to be irrep-n. If all these sub-tiles are of different sizes then the tiling ...
move to sidebar hide. This article does not cite any sources. Please help improve this article by adding citations to reliable sources. Unsourced material may be ...