\documentclass{article}
\usepackage{tikz}
\usepackage{tikz-3dplot}
\usetikzlibrary{patterns}

\begin{document}

\tdplotsetmaincoords{70}{120}
\begin{tikzpicture}[tdplot_main_coords]
\def\BigSide{5}
\def\SmallSide{1.5}
\pgfmathsetmacro{\CalcSide}{\BigSide-\SmallSide}

% The vertex at V
\tdplotsetcoord{P}{sqrt(3)*\BigSide}{55}{45}

\coordinate (sxl) at (\BigSide,\CalcSide,\BigSide);
\coordinate (syl) at (\CalcSide,\CalcSide,\BigSide);
\coordinate (szl) at (\CalcSide,\BigSide,\BigSide);

\draw[dashed] 
  (0,0,0) -- (Px)
  (0,0,0) -- (Py)
  (0,0,0) -- (Pz);
\draw[->] 
  (Px) -- ++ (1,0,0) node[anchor=north east]{$x$};
\draw[->]
   (Py) -- ++(0,1,0) node[anchor=north west]{$y$};
\draw[->] 
  (Pz) -- ++(0,0,1) node[anchor=south]{$z$};

\draw[thick]
  (Pxz) -- (P) -- (Pxy) -- (Px) -- (Pxz) -- (Pz) -- (Pyz) -- (P); 
\draw[thick]
  (Pyz) -- (Py) -- (Pxy);


\end{tikzpicture}

\end{document}