Face diagonal
id:
face-diagonal-181-882206
title:
Face diagonal
text:
In geometry, a face diagonal of a polyhedron is a diagonal on one of the faces, in contrast to a space diagonal passing through the interior of the polyhedron. A cuboid has twelve face diagonals (two on each of the six faces), and it has four space diagonals. The cuboid's face diagonals can have up to three different lengths, since the faces come in congruent pairs and the two diagonals on any face are equal. The cuboid's space diagonals all have the same length. If the edge lengths of a cuboid
brand slug:
wiki
category slug:
encyclopedia
description:
'"`UNIQ--templatestyles-00000023-QINU`"'For the avenue in [[Barcelona]], see [[:Avinguda Diagonal]]. [[Image:Cube diagonals.svg|thumb|right|The diagonals of a [[cube]] with side length 1. AC' (shown in blue) is a [[space diagonal]] with length '"`UNIQ--math-00000025-QINU`"', while AC (shown in red) is a [[face diagonal]] and has length '"`UNIQ--math-00000026-QINU`"'.]] A '''diagonal''' is a line joining two nonconsecutive vertices of a [[polygon]] or [[polyhedron]]. Informally, any sloping line is called diagonal. The word "diagonal" derives from the [[ancient Greek]] διαγώνιος ''diagonios'','"`UNIQ--ref-00000027-QINU`"' "from angle to angle" (from διά- ''dia-'', "through", "across" and γωνία ''gonia'', "angle", related to ''gony'' "knee"); it was used by both Strabo'"`UNIQ--ref-00000028-QINU`"' and Euclid'"`UNIQ--ref-00000029-QINU`"' to refer to a line connecting two vertices of a [[rhombus]] or [[cuboid]],'"`UNIQ--ref-0000002A-QINU`"' and later adopted into Latin as ''diagonus'' ("slanting line"). In [[mathematics]], in addition to its geometric meaning, a diagonal is also used in [[matrix (math)|matrices]] to refer to a set of entries along a diagonal line. == Non-mathematical uses == [[File:2512-échafaudage-Réunion.jpg|250px|thumb|right|A stand of basic scaffolding on a house construction site, with diagonal braces to maintain its structure]] In [[engineering]], a diagonal brace is a beam used to brace a rectangular structure (such as [[scaffolding]]) to withstand strong forces pushing into it; although called a diagonal, due to practical considerations diagonal braces are often not connected to the corners of the rectangle. [[Diagonal pliers]] are wire-cutting pliers defined by the cutting edges of the jaws intersects the joint rivet at an angle or "on a diagonal", hence the name. A [[diagonal lashing]] is a type of lashing used to bind spars or poles together applied so that the lashings cross over the poles at an angle. In [[association football]], the [[diagonal (football)|diagonal]] system of control is the method referees and assistant referees use to position themselves in one of the four quadrants of the pitch. [[File:Display size measurements.png|thumb|right|The diagonal is a common measurement of [[Two-dimensional display size|display size]].]] == Polygons == '"`UNIQ--templatestyles-0000002B-QINU`"'See also: [[:Quadrilateral#Diagonals|Quadrilateral § Diagonals]] As applied to a [[polygon]], a diagonal is a [[line segment]] joining any two non-consecutive vertices. Therefore, a [[quadrilateral]] has two diagonals, joining opposite pairs of vertices. For any [[convex polygon]], all the diagonals are inside the polygon, but for [[re-entrant polygon]]s, some diagonals are outside of the polygon. Any ''n''-sided polygon (''n'' ≥ 3), [[Convex polygon|convex]] or [[Concave polygon|concave]], has :'"`UNIQ--math-0000002C-QINU`"' or :'"`UNIQ--math-0000002D-QINU`"' diagonals, as each vertex has diagonals to all other vertices except itself and the two adjacent vertices, or ''n'' − 3 diagonals. {
original url:
https://en.wikipedia.org/wiki/Face_diagonal
date created:
2007-04-22T12:11:04Z
date modified:
2024-09-05T23:12:44Z
main entity:
{"identifier":"Q386387","url":"https://www.wikidata.org/entity/Q386387"}
image:
{"content_url":"https://upload.wikimedia.org/wikipedia/commons/5/57/Cube_diagonals.svg","width":275,"height":265}
fields total:
13
integrity:
16