@marmot, re: [your answer](#a1761), If I use
```
\documentclass[tikz,border=3mm]{standalone}
\usepackage{tikz-3dplot}
\usetikzlibrary{3dtools}% https://github.com/marmotghost/tikz-3dtools
\usepackage{tikz-3dplot-circleofsphere}
\begin{document}
\tdplotsetmaincoords{70}{120}
\begin{tikzpicture}[tdplot_main_coords,scale=1,line cap=butt,
line join=round,declare function={a=3;R=a/2; angC =-20;h=a;},
tdplotCsBack/.style={cheating dash},
visible/.style={draw,solid},
hidden/.style={draw,very thin,cheating dash}]
\path
(0,0,0) coordinate (A)
(5,0,0) coordinate (B)
(5, 6,0) coordinate (C)
(2,0,5) coordinate (S);
\path[3d/circumcircle center={A={(A)},B={(B)},C={(C)}}]
coordinate (G);
\path[3d/circumcircle center={A={(A)},B={(B)},C={(S)}}]
coordinate (I);
\path [3d coordinate={(M) = 0.5*(A) + 0.5*(B)}];
%\path [3d coordinate={(M) = 0.5*(A) + 0.5*(B)}, 3d coordinate={(myn1)=(A)-(B)x(A)-(C)},
%3d coordinate={(myn2)=(S)-(A)x(S)-(B)}];
%3d/line with direction={(myn2) through (I) named d2}];
\path [3d coordinate={(myn1)=(0,0,1)},
3d coordinate={(myn2)=(0,1,0)}];
\path[3d/line with direction={(myn1) through (G) named d1},
3d/line with direction={(myn2) through (I) named d2}];
\path[3d/intersection of={d1 with d2}] coordinate (T);
\foreach \p in {A,B,C,S,G,I,M,T}
\draw[fill=black] (\p) circle (1.2 pt);
\foreach \p/\g in {G/-90,A/-90,B/-90,S/90,C/-90,I/90,M/-90,T/90}
\path (\p)+(\g:3mm) node{$\p$};
\draw[hidden] (I) -- (M) -- (G) -- (T) -- cycle
(A) -- (B) -- (C) --cycle
(B) -- (I)
(S) --(A) (S) --(B) (S)--(C)
;
\end{tikzpicture}
\end{document}
```
I get correct result.