I am trying to draw Heronian Tetrahedron at http://mathworld.wolfram.com/HeronianTetrahedron.html. I cannot get the exact results with the message "Dimension too large" of the point S
. How can I get the correct result?
\documentclass[tikz,border=2 mm,12pt]{standalone}
\usepackage{tikz-3dplot-circleofsphere}
\begin{document}
\tdplotsetmaincoords{75}{150}
\begin{tikzpicture}[scale=1/10,line cap=butt,line join=round,tdplot_main_coords,declare function={R= 17*sqrt(7801)*(1/18);r=689/10;
Angle=acos(r/R);%
}]
\path
coordinate (A) at (-117/2, 182/5, 2116/45)
coordinate (B) at (117/2, 182/5, 2116/45)
coordinate (C) at (399/26, 4366/65, 2116/45)
coordinate (S) at (495/26, 8134/325, 17384/225)
coordinate (O) at (0,0,0)
coordinate (T) at (0,0, 2116/45)
coordinate (D) at (-117/2, -182/5, 2116/45);
\begin{scope}[tdplot_screen_coords]
\draw[thick] (O) circle (R);
\end{scope}
\begin{scope}
\tdplotCsDrawLatCircle[tdplotCsFront/.style={thick}]{R}{{Angle}}
\tdplotCsDrawLonCircle[tdplotCsFront/.style={thick}]{R}{atan(-45/28)}
\end{scope}
\foreach \p in {A,B,C,S,O,T,D}
\draw[fill=black] (\p) circle (15 pt);
\foreach \p/\g in {A/-90,B/45,C/-90,S/150,O/90,T/0,D/60}
\path (\p)+(\g:30mm) node{$\p$};
\foreach \X in {A,B,C} \draw[dashed] (\X) -- (S);
\draw[dashed] (A) -- (B) -- (C) -- cycle (A) -- (C) ;
\end{tikzpicture}
\end{document}