Graphics, Figures & Tables ⇒ creating a labeled tetrahedron with tikzpicture

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I am wanting to draw a tetrahedron with labeled points on each corner. I attempted to edit the example of a cone that I found here: http://www.texample.net/tikz/examples/cone/
I have made it look partially like a tetrahedron but have not been able to get it right (let alone labeled points). Any help would be appreciated, my code is below. Thanks, Brian

Code: Select all

\begin{tikzpicture}[tdplot_main_coords]
\def\RI{2}
\def\RII{1.25}

\draw[] (\RI,0)
  \foreach \x in {0,240} { --  (\x:\RI) node at (\x:\RI) (R1-\x) {} };
\draw[dashed,thick] (R1-0.center)
  \foreach \x in {120} { --  (\x:\RI) node at (\x:\RI) (R1-\x) {} };


\begin{scope}[yshift=2cm]
\draw[thick,fill=gray!30,opacity=0.2] (\RII,0)
  \foreach \x in {0,120,240,360}
    { --  (\x:\RII) node at (\x:\RII) (R2-\x) {}};
\end{scope}

\foreach \x in {0,240} { \draw (R1-\x.center)--(R2-\x.center); };
\foreach \x in {120} { \draw[dashed] (R1-\x.center)--(R2-\x.center); };
\end{tikzpicture}