\documentclass{article}
\makeatletter
\DeclareFontEncoding{LS1}{}{}
\DeclareFontSubstitution{LS1}{stix}{m}{n}
\DeclareSymbolFont{symbols}{LS1}{stixscr}  {m} {n}
\def\stix@undefine#1{%
    \if\relax\noexpand#1\let#1=\@undefined\fi}
\def\stix@MathSymbol#1#2#3#4{%
    \stix@undefine#1%
    \DeclareMathSymbol{#1}{#2}{#3}{#4}}
\stix@MathSymbol{\lrblacktriangle}{\mathord}{symbols}{"F9}
\stix@MathSymbol{\llblacktriangle}{\mathord}{symbols}{"FA}
\stix@MathSymbol{\ulblacktriangle}{\mathord}{symbols}{"FB}
\stix@MathSymbol{\urblacktriangle}{\mathord}{symbols}{"FC}
\makeatother
\begin{document}
\[
  x^{2} + \lrblacktriangle^{2} = z^{2}, x^{2} + \llblacktriangle^{2} = z^{2}, x^{2} + \ulblacktriangle^{2} = z^{2}, x^{2} + \urblacktriangle^{2} = z^{2}
\]
\end{document}