In geometry, the triangular tiling or triangular tessellation is one of the three regular tilings of the Euclidean plane, and is the only such tiling where the constituent shapes are not parallelogons. Because the internal angle of the equilateral triangle is 60 degrees, six triangles at a point occupy a full 360 degrees. The triangular tiling has Schläfli symbol of {3,6}.
English mathematician John Conway called it a deltille, named from the triangular shape of the Greek letter delta (Δ). The triangular tiling can also be called a kishextille by a kis operation that adds a center point and triangles to replace the faces of a hextille.
It is one of three regular tilings of the plane. The other two are the square tiling and the hexagonal tiling.
geometry, the triangulartiling or triangular tessellation is one of the three regular tilings of the Euclidean plane, and is the only such tiling where the...
is one of three regular tilings of the plane. The other two are the triangulartiling and the square tiling. Hexagonal tiling is the densest way to arrange...
The cantitruncated triangulartiling honeycomb, , has truncated trihexagonal tiling, truncated hexagonal tiling, and triangular prism cells, with a mirrored...
trihexagonal tiling can be geometrically distorted into topologically equivalent tilings of lower symmetry. In these variants of the tiling, the edges do...
topologically distinct. (The truncated triangulartiling is topologically identical to the hexagonal tiling.) This tiling is topologically related as a part...
the hexagonal tiling honeycomb is {6,3,3}. Since that of the hexagonal tiling is {6,3}, this honeycomb has three such hexagonal tilings meeting at each...
In geometry, the elongated triangulartiling is a semiregular tiling of the Euclidean plane. There are three triangles and two squares on each vertex...
A2 Coxeter planes. The octahedron can also be represented as a spherical tiling, and projected onto the plane via a stereographic projection. This projection...
tetrahedra or tetrahedrons), also known as a triangular pyramid, is a polyhedron composed of four triangular faces, six straight edges, and four vertices...
degenerate into edges, a triangulartiling results, constructed as a snub triangulartiling, . There is one related 2-uniform tiling, having hexagons dissected...
regular tilings of the plane. The other two are the triangulartiling and the hexagonal tiling. There are 9 distinct uniform colorings of a square tiling. Naming...
truncated trihexagonal tiling has three related 2-uniform tilings, one being a 2-uniform coloring of the semiregular rhombitrihexagonal tiling. The first dissects...
wallpaper groups. A tiling that lacks a repeating pattern is called "non-periodic". An aperiodic tiling uses a small set of tile shapes that cannot form...
Euclidean 3-space. It is composed entirely of triangular prisms. It is constructed from a triangulartiling extruded into prisms. It is one of 28 convex...
continues as the trihexagonal tiling, vertex figure (3.6)2 - a quasiregular tiling based on the triangulartiling and hexagonal tiling. The checkerboard pattern...
volume of all pyramids with the base of triangular faces and the height with the distance from a triangular face's centroid to the center inside the...
hyperbolic geometry, a uniform hyperbolic tiling (or regular, quasiregular or semiregular hyperbolic tiling) is an edge-to-edge filling of the hyperbolic...
called bihedra, flat polyhedra, or doubly covered polygons. As a spherical tiling, a dihedron can exist as nondegenerate form, with two n-sided faces covering...
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