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...is a [[centered triangular number]].<ref>{{Cite OEIS|A005448|name=Centered triangular numbers}}</ref> ...e/pii/S0012365X14003288 |title=Uniform edge-c-colorings of the Archimedean tilings |journal=Discrete Mathematics |volume=338 |issue=1 |pages=19–22 |date=Janua ...

...lizers|orbits]] of vertices.<ref>{{Cite OEIS |A068599 |Number of n-uniform tilings. |access-date=2023-01-07 }}</ref> ...or equivalently the 36th [[triangular number]].<ref>{{Cite OEIS |A000217 |Triangular numbers |access-date=2022-11-05 }}</ref> ...

...es#Euclidean tilings|regular]] and 8 [[List of uniform tilings|semiregular tilings]] in the plane. An alternate truncation deletes every other vertex, creating a new triangular faces at the removed vertices, and reduces the original faces to half as ma ...

Cantellation (for polyhedra and tilings) is also called ''[[Expansion (geometry)|expansion]]'' by [[Alicia Boole St == Examples: cantellating polyhedra, tilings == ...

...e]] is 60 degrees, six triangles at a point occupy a full 360 degrees. The triangular tiling has [[Schläfli symbol]] of {{math|{3,6}.}} ...the triangular shape of the Greek letter [[Delta (letter)|delta]] (Δ). The triangular tiling can also be called a '''kishextille''' by a [[Conway kis operator|ki ...

...es#Euclidean tilings|regular]] and 8 [[List of uniform tilings|semiregular tilings]] in the plane. == Topologically identical tilings== ...

...s and two squares on each [[vertex (geometry)|vertex]]. It is named as a [[triangular tiling]] [[elongation (geometry)|elongated]] by rows of squares, and given ...es#Euclidean tilings|regular]] and 8 [[List of uniform tilings|semiregular tilings]] in the plane. This tiling is similar to the [[snub square tiling]] which ...

...ihexagonal tiling''' is one of eight [[List of uniform tilings|semiregular tilings]] of the Euclidean plane. There are one [[Square (geometry)|square]], one [ * Omnitruncated hexagonal tiling, omnitruncated triangular tiling ...

...ces and its octagonal faces are parallel to those of a [[cube]], while its triangular faces are parallel to those of an [[octahedron]]: hence the name ''cubicubo ...y shares its [[edge arrangement]] with the rhombicuboctahedron (having the triangular faces and 6 square faces in common), and with the [[small rhombihexahedron] ...

...the [[dual polyhedra]], the set of [[gyroelongated dipyramid]]s, have all triangular faces. For example, the [[icosahedron]] is the dual of the [[dodecahedron]] [[File:Triangular truncated trapezohedron.png|100px]] ...

[[File:Brückner Vielflache Fig. 96b - 98.jpg|thumb|Uniform tilings and their duals drawn by [[Max Brückner]] in ''Vielecke und Vielflache '' ( ...semiregular) of the [[Euclidean geometry|Euclidean plane]], and their dual tilings. ...

...uclidean tilings|regular]] and eight [[List of uniform tilings|semiregular tilings]] in the plane. ...enerate into edges, a [[triangular tiling]] results, constructed as a snub triangular tiling, {{CDD|node_h|3|node_h|6|node}}. ...

...square grid. A triangular polystick is a connected subset of a regular triangular grid. Polysticks are classified according to how many line segments they c ...tro.html</ref> has been proposed by David Goodger to simplify the phrases "triangular-grid polysticks" and "hexagonal-grid polysticks," respectively. Colin F. Br ...

...uclidean tilings|regular]] and eight [[List of uniform tilings|semiregular tilings]] in the plane. This is the only one which does not have a reflection as a ...leading to the densest packing from the [[triangular tiling#circle packing|triangular tiling]]. ...

| title = The Tiling Book: An Introduction to the Mathematical Theory of Tilings | title = Tilings and Patterns ...

...rm polyhedra. However, the construction methods do not lead to all uniform tilings in Euclidean or hyperbolic space. ...sible. The symbol that would normally refer to that is reused for the snub tilings. ...

.... The pyramid heights are adjusted to make them coplanar with the other 24 triangular faces of the snub cube. The result is the pentagonal icositetrahedron. ...6 square faces and 8 triangular faces of a [[snub cube]] such that the new triangular faces with 3 coplanar triangles merged into identical pentagon faces. ...

...e fully, ''trigonal trisoctahedron''. Both names reflect that it has three triangular faces for every face of an octahedron. The ''tetragonal trisoctahedron'' is The triakis octahedron is a part of a sequence of polyhedra and tilings, extending into the hyperbolic plane. These [[face-transitive]] figures hav ...

== In polyhedra and plane tilings == |[[Image:Uniform tiling 63-t2.svg|75px]]<BR>[[Triangular tiling]] ...

.... The pyramid heights are adjusted to make them coplanar with the other 60 triangular faces of the snub dodecahedron. The result is the pentagonal hexecontahedro ...faces and 20 triangular faces of a [[snub dodecahedron]] such that the new triangular faces are coparallel to other triangles and can be merged into the pentagon ...