dihedral angleDihedralAngle2009-02-04 07:29:292009-08-14 21:35:56Definitionangle between two planesedgesidenormal sectionconcaveperpendicularperpendicular planes% this is the default PlanetMath preamble. as your knowledge
% of TeX increases, you will probably want to edit this, but
% it should be fine as is for beginners.
% almost certainly you want these
\usepackage{amssymb}
\usepackage{amsmath}
\usepackage{amsfonts}
% used for TeXing text within eps files
%\usepackage{psfrag}
% need this for including graphics (\includegraphics)
%\usepackage{graphicx}
% for neatly defining theorems and propositions
\usepackage{amsthm}
% making logically defined graphics
%\usepackage{xypic}
\usepackage{pstricks}
\usepackage{pst-plot}
% there are many more packages, add them here as you need them
% define commands here
\theoremstyle{definition}
\newtheorem*{thmplain}{Theorem}
Two distinct half-planes, emanating from a same line $l$, \PMlinkescapetext{divide} the space ($\mathbb{R}^3$) into two regions called {\em dihedral angles}.\, The line $l$ is the {\em edge} of the dihedral angle and the bounding half-planes are its {\em sides}.
\begin{center}
\begin{pspicture}(-3,-1)(3,3)
\psline[linewidth=0.05](-2.5,-1)(1.5,-1)(2.5,0)(2,2)(-2,2)
\psline(-2,2)(-1.5,0)(-2.5,-1)
\psline(-2.1,0)(3,0)
\rput(0,0.2){$l$}
\end{pspicture}
\end{center}
The angle, which the sides of a dihedral planes separate from a normal plane of the edge, is the {\em normal section} of the dihedral angle.\, Apparently, all normal sections are equal.\, According to the \PMlinkescapetext{size} of the normal section, the dihedral angle may be called acute, right, obtuse, straight, \PMlinkname{skew}{ConvexAngle}, convex and concave.\, Unlike the angle between two planes, a dihedral angle may be over 90 \PMlinkescapetext{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 {\em perpendicular} to each other.