Rounded Corners via Circle that leaves a trace

In the following code, the edges do not align very well. I would like to have rounded corners. Imagine a black circle with the thickness of the line, leaving behind a trace, where the center of that circle follows the specified path. Does someone know a solution?

    documentclass{standalone}
    
    usepackage{tikz}
    
    begin{document}
         begin{tikzpicture}
              coordinate (000) at (0, 0, 0);
              coordinate (001) at (0, 0, -1);
              coordinate (010) at (0, 1, 0);
              coordinate (011) at (0, 1, -1);
              coordinate (100) at (1, 0, 0);
              coordinate (101) at (1, 0, -1);
              coordinate (110) at (1, 1, 0);
              coordinate (111) at (1, 1, -1);
    
              draw[thick, line cap = round, rounded corners = 0.8pt] (100) -- (000) -- (111) -- (100) -- (101) -- (111);
          end{tikzpicture}
      end{document}