Triangular tiling: Difference between revisions

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Revision as of 06:02, 28 May 2022

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{{short description|Regular tiling of the plane}}

{{Uniform tiles db|Reg tiling stat table|Ut}}

In [[geometry]], the '''triangular tiling''' or '''triangular tessellation''' is one of the three regular [[tessellation|tiling]]s of the [[Euclidean plane]], and is the only such tiling where the constituent shapes are not [[parallelogon]]s. 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}.

In [[geometry]], the '''triangular tiling''' or '''triangular tessellation''' is one of the three regular [[tessellationTessellation|tilingtilings]]s of the [[Euclidean plane]], and is the only such tiling where the constituent shapes are not [[parallelogon]]s. Because the internal angle of the equilateral [[equilateral triangle]] is 60 degrees, six triangles at a point occupy a full 360 degrees. The triangular tiling has [[Schläfli symbol]] of {{math|{3,6}.}}

[[John Horton Conway|Conway]] calls 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 [[Conway kis operator|kis]] operation that adds a center point and triangles to replace the faces of a [[hextille]].

English mathematician [[John Horton Conway|John Conway]] callscalled it a '''deltille''', named from 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|kis]] operation that adds a center point and triangles to replace the faces of a [[hextille]].

It is one of [[List of regular polytopes#Euclidean tilings|three regular tilings of the plane]]. The other two are the [[square tiling]] and the [[hexagonal tiling]].