Overlay diagrams in TikZ

Question

I want to join the vertices labeled as (1), b, abc, and ac but could not succeed. I'd highly appreciate if you point me out what I'm doing wrong and what is the solution. Thanks

\documentclass{standalone}
\usepackage{tikz}
\usetikzlibrary{calc}
\begin{document}
\begin{tikzpicture}[scale = 4, fill opacity = 1.0, thick,
                        line cap = round, line join = round]
    %% Define coordinate labels.
    % t(op) and b(ottom) layers
    \path \foreach \layer/\direction in {b/{0, 0, 0}, t/{0, 1, 0}} {
        (\direction)
        \foreach \point/\label in {{0, 0, 0}/ll, {1, 0, 0}/lr, {1, 0, -1}/ur, {0, 0, -1}/ul} {
            +(\point) coordinate (\layer\label)
        }
        ($(\layer ll)!0.5!(\layer ur)$) coordinate (\layer md)
    };



    % Put text next to the labels as requested.
    % Funilly enough we need to set fill opacity to 1.
    \draw \foreach \text/\label/\anchor in {%
        $\left(1\right)$/bll/east,
        $b$/bul/east,
        $c$/tll/east,
        $bc$/tul/east,
        $a$/blr/west,
        $ab$/bur/west,
        $ac$/tlr/west,
        $abc$/tur/west} {
        (\label) node[anchor=\anchor, fill opacity = 1] {\text}
    };
    % Draw  cube.
    \fill (0, 0, -1) circle (0.5pt);
    \foreach \direction in {(0, 0, 1), (0, 1, 0), (1, 0, 0)} {
        \draw[dashed, black] (bul) -- + \direction;
    }


    \fill[red!60,   opacity=0.5]  (tll) -- (tul)  -- (bur) -- (blr);
    \fill[blue!60, opacity=0.5]  (bll)   -- (bul)   -- (tur) -- (tlr);




    \draw (bll) -- (blr) -- (tlr) -- (tll) -- cycle;
    \draw (blr) -- (bur) -- (tur) -- (tlr) -- cycle;
    \draw (tll) -- (tlr) -- (tur) -- (tul) -- cycle;

    \foreach \point in {bll, blr, bur, tll, tlr, tul, tur} {
        \fill[fill opacity=1] (\point) circle (0.75pt);
    }


\node[below] at (1.0, -0.2, 0.0) {$AC$};

\end{tikzpicture}
\end{document}

Answer 1

Simply change the z-direction so that the points are no longer apparently collinear.

\documentclass{standalone}
\usepackage{tikz}
\usetikzlibrary{calc}

\begin{document}
\begin{tikzpicture}[scale = 4, thick,
    % change the z-direction
    z={(-0.3,-0.6)}]

    %% Define coordinate labels.
    % t(op) and b(ottom) layers
    \path \foreach \layer/\direction in {b/{0, 0, 0}, t/{0, 1, 0}} {
        (\direction)
        \foreach \point/\label in {{0, 0, 0}/ll, {1, 0, 0}/lr, {1, 0, -1}/ur, {0, 0, -1}/ul} {
            +(\point) coordinate (\layer\label)
        }
        ($(\layer ll)!0.5!(\layer ur)$) coordinate (\layer md)
    };

    % Put text next to the labels as requested.
    \draw \foreach \text/\label/\anchor in {%
        $\left(1\right)$/bll/east,
        $b$/bul/east,
        $c$/tll/east,
        $bc$/tul/east,
        $a$/blr/west,
        $ab$/bur/west,
        $ac$/tlr/west,
        $abc$/tur/west} {
        (\label) node[anchor=\anchor] {\text}
    };
    % Draw  cube.
    \fill (0, 0, -1) circle (0.5pt);
    \foreach \direction in {(0, 0, 1), (0, 1, 0), (1, 0, 0)} {
        \draw[dashed, black] (bul) -- + \direction;
    }

    % add some midpoints for correct drawing of transparent planes
    \coordinate (m1) at ($(bll)!0.5!(tlr)$);
    \coordinate (m2) at ($(bul)!0.5!(tur)$);

    \fill[blue!60, opacity=0.5]  (bll)   -- (bul)   -- (m2) -- (m1) -- cycle;
    \fill[red!60,   opacity=0.5]  (tll) -- (tul)  -- (bur) -- (blr) -- cycle;
    \fill[blue!60, opacity=0.5]  (m1) -- (m2) -- (tur) -- (tlr) -- cycle;
    \draw[very thin, black!60] (m1) -- (m2);

    \draw (bll) -- (blr) -- (tlr) -- (tll) -- cycle;
    \draw (blr) -- (bur) -- (tur) -- (tlr) -- cycle;
    \draw (tll) -- (tlr) -- (tur) -- (tul) -- cycle;

    \foreach \point in {bll, blr, bur, tll, tlr, tul, tur} {
        \fill[fill opacity=1] (\point) circle (0.75pt);
    }
\end{tikzpicture}
\end{document}