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dihedral angle
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(Definition)
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Two distinct half-planes, emanating from a same line $l$ , divide the space ($\mathbb{R}^3$ ) into two regions called dihedral angles. The line $l$ is the edge of the dihedral angle and the bounding half-planes are its sides.
The angle, which the sides of a dihedral planes separate from a normal plane of the edge, is the normal section of the dihedral angle. Apparently, all normal sections are equal. According to the size of the normal section, the dihedral angle may be called acute, right, obtuse, straight, skew, convex and concave. Unlike the angle between two planes, a dihedral angle may be over 90 degrees.
If two planes intersect each other and if one of the four dihedral angles formed is right, then also the others are right. Then we say that the planes are perpendicular to each other.
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"dihedral angle" is owned by pahio.
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Cross-references: intersect, angle between two planes, convex, straight, obtuse, right, acute, normal plane, planes, angle, regions, line
There are 131 references to this entry.
This is version 5 of dihedral angle, born on 2009-02-04, modified 2009-08-14.
Object id is 11602, canonical name is DihedralAngle.
Accessed 2482 times total.
Classification:
| AMS MSC: | 51M04 (Geometry :: Real and complex geometry :: Elementary problems in Euclidean geometries) |
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Pending Errata and Addenda
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(1.5,-1)(2.5,0)(2,... ...ne(-2,2)(-1.5,0)(-2.5,-1) \psline(-2.1,0)(3,0) \rput(0,0.2){$l$} \end{pspicture}](http://images.planetmath.org:8080/cache/objects/11602/js/img1.png "\begin{pspicture}(-3,-1)(3,3) \psline[linewidth=0.05](-2.5,-1)(1.5,-1)(2.5,0)(2,... ...ne(-2,2)(-1.5,0)(-2.5,-1) \psline(-2.1,0)(3,0) \rput(0,0.2){$l$} \end{pspicture}"){kind=small}