TikZ wrong perspective

Question

The perspective looks wrong. What's going on?
(Also, feel free to comment on anything that could be improved.)

\documentclass{standalone}
\usepackage{tikz}\usetikzlibrary{calc}
\pagecolor{darkgray}\color{white}
\begin{document}
\begin{tikzpicture}[
  scale = 5,
  rotate around y = 50,
  dot/.style = {
    fill, draw, circle,
    inner sep = 0,
    minimum size = 2pt,
  }
]

  \node [dot] (O) at (0, 0, 0) {};
  \filldraw [
    color = green,
    fill opacity = 0.25,
  ]
    (1,0,0) node [dot] (i) {} --
    (0,1,0) node [dot] (j) {} --
    (0,0,1) node [dot] (k) {} --
    cycle;
  \draw [->] (O) -- ($1.3*(i)$);
  \draw [->] (O) -- ($1.3*(j)$);
  \draw [->] (O) -- ($1.3*(k)$);

\end{tikzpicture}
\end{document}

Here is a version with a rotation of 30 instead.

The objective is the one below.

Answer 1

\documentclass[tikz, border=1cm]{standalone}
\usetikzlibrary{calc}
\pagecolor{darkgray}\color{white}
\begin{document}
\begin{tikzpicture}[
   x={(5,1)}, y={(0,4.3)}, z={(0.3,-0.8)},
   dot/.style = {
    fill, draw, circle,
    inner sep = 0,
    minimum size = 2pt,
  }
]

  \node [dot] (O) at (0, 0, 0) {};
  \filldraw [
    color = green,
    fill opacity = 0.25,
  ]
    (1,0,0) node [dot] (i) {} --
    (0,1,0) node [dot] (j) {} --
    (0,0,1) node [dot] (k) {} --
    cycle;
  \draw [->] (O) -- ($1.3*(i)$);
  \draw [->] (O) -- ($1.3*(j)$);
  \draw [->] (O) -- ($1.3*(k)$);

\end{tikzpicture}
\end{document}