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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 ]
Example tessellation based on a Type 1 hexagonal tile. In its simplest form, the criterion simply states that any hexagon with a pair of opposite sides that are parallel and congruent will tessellate the plane. [8] In Gardner's article, this is called a type 1 hexagon. [7] This is also true of parallelograms.
The tesseract can make a regular tessellation of 4-dimensional hyperbolic space, with 5 tesseracts around each face, with Schläfli symbol {4,3,3,5}, called an order-5 tesseractic honeycomb. The Ammann–Beenker tiling is an aperiodic tiling in 2 dimensions obtained by cut-and-project on the tesseractic honeycomb along an eightfold rotational ...
Convex uniform honeycomb – The 28 uniform 3-dimensional tessellations, a parallel construction to the convex uniform Euclidean plane tilings. Euclidean tilings by convex regular polygons; List of tessellations; Percolation threshold; Uniform tilings in hyperbolic plane
Create account; Log in; Personal tools. Donate; Create account; ... This is a list of tessellations. This list is incomplete; you can help by adding missing items.
The cubic honeycomb or cubic cellulation is the only proper regular space-filling tessellation (or honeycomb) in Euclidean 3-space made up of cubic cells. It has 4 cubes around every edge, and 8 cubes around each vertex. Its vertex figure is a regular octahedron. It is a self-dual tessellation with Schläfli symbol {4,3,4}.
The tetrahedral-octahedral honeycomb, alternated cubic honeycomb is a quasiregular space-filling tessellation (or honeycomb) in Euclidean 3-space. It is composed of alternating regular octahedra and tetrahedra in a ratio of 1:2. Other names include half cubic honeycomb, half cubic cellulation, or tetragonal disphenoidal cellulation.
In the geometry of tessellations, a rep-tile or reptile is a shape that can be dissected into smaller copies of the same shape. The term was coined as a pun on animal reptiles by recreational mathematician Solomon W. Golomb and popularized by Martin Gardner in his " Mathematical Games " column in the May 1963 issue of Scientific American . [ 1 ]
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