Editing Equilateral triangle (section)

=== In other related figures ===
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 | image1 = Tiling 3 simple.svg
 | caption1 = The equilateral triangle tiling fills the plane
 | image2 = Sierpinski triangle.svg
 | caption2 = The Sierpiński triangle
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Notably, the equilateral triangle [[Euclidean tilings by convex regular polygons#Regular tilings|tiles]] the [[Euclidean plane]] with six triangles meeting at a vertex; the dual of this tessellation is the [[hexagonal tiling]]. [[Truncated hexagonal tiling]], [[rhombitrihexagonal tiling]], [[trihexagonal tiling]], [[snub square tiling]], and [[snub hexagonal tiling]] are all [[Euclidean tilings by convex regular polygons#Archimedean, uniform or semiregular tilings|semi-regular tessellations]] constructed with equilateral triangles.{{sfnp|Grünbaum|Shepard|1977}} Other two-dimensional objects built from equilateral triangles include the [[Sierpiński triangle]] (a [[Fractal|fractal shape]] constructed from an equilateral triangle by subdividing recursively into smaller equilateral triangles) and [[Reuleaux triangle]] (a [[Circular triangle|curved triangle]] with [[Curve of constant width|constant width]], constructed from an equilateral triangle by rounding each of its sides).{{sfnp|Alsina|Nelsen|2010|p=[https://books.google.com/books?id=mIT5-BN_L0oC&pg=PA102 102&ndash;103]}}

[[File:Octahedron.jpg|thumb|left|200px|The regular octahedron is a [[deltahedron]], as well as a member of the family of [[antiprism]]s.]]
Equilateral triangles may also form a polyhedron in three dimensions. A polyhedron whose faces are all equilateral triangles is called a [[deltahedron]].  There are eight [[convex set|strictly convex]] deltahedra: three of the five [[Platonic solid]]s ([[regular tetrahedron]], [[regular octahedron]], and [[regular icosahedron]]) and five of the 92 [[Johnson solid]]s ([[triangular bipyramid]], [[pentagonal bipyramid]], [[snub disphenoid]], [[triaugmented triangular prism]], and [[gyroelongated square bipyramid]]).{{sfnp|Trigg|1978}} More generally, all [[Johnson solid]]s have equilateral triangles among their faces, though most also have other other [[regular polygon]]s.{{sfnp|Berman|1971}}

The [[antiprism]]s are a family of polyhedra incorporating a band of alternating triangles. When the antiprism is [[Uniform polyhedron|uniform]], its bases are regular and all triangular faces are equilateral.{{sfnp|Horiyama|Itoh|Katoh|Kobayashi|2015|p=[https://books.google.com/books?id=L9WSDQAAQBAJ&pg=PA124 124]}}

As a generalization, the equilateral triangle belongs to the infinite family of <math>n</math>-[[simplex (geometry)|simplexes]], with <math>n = 2</math>.{{sfnp|Coxeter|1948|p=120&ndash;121}}
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