Triangular tiling: Difference between revisions

Revision as of 03:34, 5 November 2020

Revision as of 22:16, 6 September 2021

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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}.

[[John Horton Conway|Conway]] calls it a '''deltilledeltile''', named from the triangular shape of the Greek letter delta (Δ). The triangular tiling can also be called a '''kishextillekishextile''' by a [[Conway kis operator|kis]] operation that adds a center point and triangles to replace the faces of a [[hextillehextile]].

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]].

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{| class=wikitable

|- align=center valign=bottom

|[[File:1-uniform 3 dual.svg|240px]]<br/>[[KisrhombilleKisrhombile tiling|KisrhombilleKisrhombile]]<BR/>30°-60°-90° right triangles

|[[File:1-uniform 2 dual.svg|240px]]<br/>[[Tetrakis square tiling|KisquadrilleKisquadrile]]<BR/>45°-45°-90° right triangles

|[[File:1-uniform 4 dual.svg|240px]]<br/>[[Triakis triangular tiling|Kisdeltile]]<BR/>30°-30°-120° isosceles triangles

|}