Editing Triangle (section)

== Appearances ==
[[File:Triangular dipyramid.png|thumb|A [[triangular bipyramid]] can be constructed by attaching two [[tetrahedron|tetrahedra]]. This polyhedron can be said to be a [[simplicial polyhedron]] because all of its faces are triangles. More specifically, when the faces are equilateral, it is categorized as a [[deltahedron]].]]
All types of triangles are commonly found in real life. In man-made construction, the isosceles triangles may be found in the shape of [[gable]]s and [[pediment]]s, and the equilateral triangle can be found in the yield sign.<ref>{{multiref
|{{harvp|Lardner|1840|p=46}}
|{{harvnb|Riley|Cochran|Ballard|1982}}
}}</ref> The faces of the [[Great Pyramid of Giza]] are sometimes considered to be equilateral, but more accurate measurements show they are isosceles instead.{{sfnp|Herz-Fischler|2000|p=}} Other appearances are in [[heraldic]] symbols as in the [[flag of Saint Lucia]] and [[flag of the Philippines]].{{sfnp|Guillermo|2012|p=[https://books.google.com/books?id=wmgX9M_yETIC&pg=PA161 161]}}

Triangles also appear in three-dimensional objects. A [[polyhedron]] is a solid whose boundary is covered by flat [[polygonal]]s known as the faces, sharp corners known as the vertices, and line segments known as the edges. Polyhedra in some cases can be classified, judging from the shape of their faces. For example, when polyhedra have all equilateral triangles as their faces, they are known as [[deltahedron|deltahedra]].{{sfnp|Cundy|1952}} [[Antiprism]]s have alternating triangles on their sides.{{sfnp|Montroll|2009|p=[https://books.google.com/books?id=SeTqBgAAQBAJ&pg=PA4 4]}} [[Pyramid (geometry)|Pyramid]]s and [[bipyramid]]s are polyhedra with polygonal bases and triangles for lateral faces; the triangles are isosceles whenever they are right pyramids and bipyramids. The [[Kleetope]] of a polyhedron is a new polyhedron made by replacing each face of the original with a pyramid, and so the faces of a Kleetope will be triangles.<ref>{{multiref
|{{harvp|Lardner|1840|p=46}}
|{{harvp|Montroll|2009|p=[https://books.google.com/books?id=SeTqBgAAQBAJ&pg=PA6 6]}}
}}</ref> More generally, triangles can be found in higher dimensions, as in the generalized notion of triangles known as the [[simplex]], and the [[polytope]]s with triangular [[facet]]s known as the [[simplicial polytope]]s.{{sfnp|Cromwell|1997|p=341}}