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| [[Image:Cube diagonals.svg|thumb|right|250px|AC (shown in red) is a face diagonal while AC' (shown in blue) is a [[space diagonal]]]]
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| In [[geometry]], a '''face diagonal''' of a [[polyhedron]] is a [[diagonal]] on one of the [[faces (geometry)|faces]], in contrast to a [[space diagonal]] passing through the interior of the polyhedron.<ref>{{citation|title=Mathematics: From the Birth of Numbers|first=Jan|last=Gullberg|publisher=W. W. Norton & Company|year=1997|isbn=9780393040029|url=http://books.google.com/books?id=E09fBi9StpQC&pg=PA396|page=396}}.</ref>
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| A [[cuboid]] has twelve face diagonals (and four space diagonals);<ref>{{citation|title=New Maths in Action|first=Edward C. K.|last=Mullan|publisher=Nelson Thornes|year=2003|isbn=9780748765195|page=220|url=http://books.google.com/books?id=roPoNOacwPkC&pg=PA220}}.</ref> the cuboid's face diagonals can have up to three different lengths (the space diagonals all have the same length). A regular [[dodecahedron]] has 60 face diagonals (and 100 space diagonals).<ref>{{citation|title=Platonic & Archimedean Solids|series=Wooden Books|first=Daud|last=Sutton|publisher=Bloomsbury Publishing USA|year=2002|isbn=9780802713865|page=55|url=http://books.google.com/books?id=vgo7bTxDmIsC&pg=PA55}}.</ref>
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| The face diagonal of a [[cube]] with side length ''a'' is <math>a\sqrt 2</math>.<ref>{{citation|title=The Essence of Materials for Engineers|first=Robert W., Jr.|last=Messler|publisher=Jones & Bartlett Publishers|year=2010|isbn=9780763778330|page=56|url=http://books.google.com/books?id=VN9BTDdOLYcC&pg=PA56}}.</ref>
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| ==References== | |
| {{reflist}}
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| [[Category:Elementary geometry]]
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| {{Elementary-geometry-stub}}
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Latest revision as of 18:33, 24 June 2014
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