Tikz Code Viewer

% Enrique Acosta
% 2020

\documentclass[border=5pt, tikz]{standalone}
\usepackage{pgfplots}
\begin{document}

\def\unitLength{4cm}

\begin{tikzpicture}[x = (10:\unitLength), 
                    y = (130:0.6*\unitLength), 
                    z = (90:\unitLength),
                    line width=0.8pt]
\usetikzlibrary{calc}
\usetikzlibrary{3d} %  To be able to use cylindrical coords

% Params
% * lines extend \extra beyond the points [1,0,0], [0,1,0], [0,0,1]
% * circle centered at (-\extra,-\extra) through (0,1) and (1,0) 
%   has radius \radius.
\pgfmathsetmacro{\extra}{0.1}
\pgfmathsetmacro{\radius}{sqrt(2*\extra^2+2*\extra+1)}

% Points
\coordinate (e0) at (0,0,0);
\coordinate (e1) at (1,0,0);
\coordinate (e2) at (0,1,0);
\coordinate (e3) at (0,0,1);

\node[below left] at (e0) {$[1,0,0,0]=(0,0,0)=e_0$};
\node[above right] at (e1) {$e_1=[0,1,0,0]$};
\node[above=7pt, left=5pt ] at (e2) {$[0,0,1,0]=e_2$};
\node[above right] at (e3) {$e_3=[0,0,0,1]$};

% Lines
\draw[shorten >=-10pt, shorten <=-10pt] 
    (e0) -- node[pos=0.4, below right]{$\overline{e_0e_1}=\{x_2=x_3=0\}$}
    (e1);

\draw[shorten >=-10pt, shorten <=-10pt]  
    (e0) -- node[midway, below left] {$\{x_1=x_3=0\}=\overline{e_0e_2}$}
    (e2);

\draw[shorten >=-10pt, shorten <=-10pt]
    (e0) -- node[pos=0.65,  right] {$\overline{e_0e_3}$}
    (e3);

% Arc notation is "(starting pt) arc ...", so (starting pt) is computed by
% adding the cylindrical coord (angle=0, radius=\radius, z=0) to the center.
\draw[dashed]
($(-\extra,-\extra,0)+(xyz cylindrical cs: angle=0, radius=\radius, z=0)$) 
arc[start angle=0, end angle=90, radius=\radius] 
node[midway, above ] {$\overline{e_1e_2}$};

% Arc notation in a different plane is "(starting pt) [x=<init vector in 1st
% coord dir>, y=<init vector in 2st coord dir>] arc ...", so (starting pt) is
% computed by adding the cylindrical coord (angle=0, radius=\radius, z=0) to
% the center.
\draw[red]
($(0,-\extra,-\extra)+(xyz cylindrical cs: angle=90, radius=\radius, z=0)$) 
[x={(0,1,0)},y={(0,0,1)}] arc [start angle=0, end angle=90, radius=\radius] 
node [pos=0.3, above left]{$\{x_0=x_1=0\}=\overline{e_2e_3}$};

\draw[blue]
($(-\extra,0,-\extra)+(xyz cylindrical cs: angle=0, radius=\radius, z=0)$) 
[x={(1,0,0)},y={(0,0,1)}] arc [start angle=0, end angle=90, radius=\radius] 
node [pos=0.4, above right]{$\overline{e_1e_3}=\{x_0=x_2=0\}$};

% Draw points
\foreach \point in {e0, e1, e2, e3}{ 
    \fill[black] (\point) circle (0.08cm);
};
\end{tikzpicture}
\end{document}