Difference between revisions of "Diagonal"
m |
|||
| Line 1: | Line 1: | ||
{{stub}} | {{stub}} | ||
| + | ==Polygons== | ||
| + | A '''diagonal''' of a [[polygon]] is any segment joining two [[vertex|vertices]] other than an [[edge]]. | ||
| − | A | + | [[Triangle]]s have no diagonals while [[convex polygon|convex]] [[quadrilateral]]s have two interior diagonals and [[concave]] quadrilaterals have on interior and one exterior diagonal. |
| + | The number of edges plus the number of diagonals of a polygon with n vertices is equal to <math>n \choose 2</math> | ||
| + | ==Polyhedra== | ||
| + | Polyhedra have two different kinds of diagonals, face diagonals and space diagonals. A face diagonal of a [[polyhedron]] is a diagonal of one of the [[face]]s of the polyhedron, while a space diagonal is any segment joining two vertices which is neither an edge nor a face diagonal. | ||
| − | [[ | + | [[Tetrahedron|Tetrahedra]] have no space or face diagonals. [[Octahedron|Octahedra]] have no face diagonals but have 3 space diagonals. [[Cube]]s have 12 face diagonals (2 on each face) and 4 space diagonals. |
| + | The number of edges plus the number of face diagonals plus the number of space diagonals of a polyhedron with n vertices is equal to <math>n \choose 2</math>. | ||
Revision as of 10:22, 13 July 2006
This article is a stub. Help us out by expanding it.
Polygons
A diagonal of a polygon is any segment joining two vertices other than an edge.
Triangles have no diagonals while convex quadrilaterals have two interior diagonals and concave quadrilaterals have on interior and one exterior diagonal.
The number of edges plus the number of diagonals of a polygon with n vertices is equal to 
Polyhedra
Polyhedra have two different kinds of diagonals, face diagonals and space diagonals. A face diagonal of a polyhedron is a diagonal of one of the faces of the polyhedron, while a space diagonal is any segment joining two vertices which is neither an edge nor a face diagonal.
Tetrahedra have no space or face diagonals. Octahedra have no face diagonals but have 3 space diagonals. Cubes have 12 face diagonals (2 on each face) and 4 space diagonals.
The number of edges plus the number of face diagonals plus the number of space diagonals of a polyhedron with n vertices is equal to .
