Drawing a central composite design

Question

Please I would like to draw a central composite design using PSTricks, or possibly tikz. This is the cube with the axes showed below. I have tried pst-3d but this is not easy. If you had an example of a similar figure this would be ideal.

EDIT (later): Ok I am back to home and I have found some time to do the figure with pst3d-plot. This is not the final figure but now it is easy to modify with the help of the pst3d-plot documentation (except that the options are not all documented e.g. for pstThreeDBox - do you know another doc?)

    \documentclass[12pt]{article}

    \usepackage{pst-all}
    \usepackage{pst-3dplot}

    \begin{document}

   \begin{pspicture}(-6,-6.5)(6 ,6)
     \psset{Alpha=30,Beta=20}
     \pstThreeDBox[fillstyle=gradient,RotSequence=xyz](-4,-4,-4)(0,8,0)(8,0,0)(0,0,8)
     \pstThreeDDot(6.7,0,0)
      \pstThreeDDot(0,6.7,0)
       \pstThreeDDot(0,0,6.7)
       \pstThreeDCoor[linecolor=black, IIIDticks, IIIDlabels,
     IIIDOffset={(0,0,0)}, 
      xMin=-7.95,  yMin=-7.95,  zMin=-7.95, 
     xMax=8,  yMax=8,  zMax=8, 
      IIIDxTicksPlane=xz, IIIDxticksep = 0.4, , Dx=1,  deltax=4,
        IIIDyTicksPlane=xz, IIIDyticksep = -0.4, , Dy=1,  deltay=4,
      IIIDzTicksPlane=xz, IIIDzticksep = -0.4, , Dz=1,   deltaz=4]
     \end{pspicture}

    \end{document}

Answer 1

Another TikZ version, using the 3D coordinate system:

Code

\documentclass[tikz,border=2mm]{standalone}

\begin{document}

\pgfmathsetmacro{\dumbbelllength}{2}

\pgfmathsetmacro{\xangle}{10}
\pgfmathsetmacro{\yangle}{130}
\pgfmathsetmacro{\zangle}{90}

\begin{tikzpicture}
[   x={(\xangle:1cm)},
    y={(\yangle:1cm)},
    z={(\zangle:1cm)},
    scale=2,
]

\foreach \x in {-1,1} \foreach \y in {-1,1} \foreach \z in {-1,1} \coordinate (c\x\y\z) at (\x,\y,\z);

\draw[fill=black,very thick] (0,1,0) -- (0,\dumbbelllength,0) circle (0.05cm);
\draw[fill=black,very thick] (1,0,0) -- (\dumbbelllength,0,0) circle (0.05cm);
\draw[fill=black,very thick] (0,0,-1) -- (0,0,-\dumbbelllength) circle (0.05cm);

\begin{scope}[fill opacity=0.5,draw=black,draw opacity=1,thick]
    \filldraw[violet,draw=black] (c-1-1-1) -- (c-11-1) -- (c11-1) -- (c1-1-1) -- cycle;
    \filldraw[red,draw=black] (c111) -- (c11-1) -- (c1-1-1) -- (c1-11) -- cycle;
    \filldraw[blue,draw=black] (c111) -- (c11-1) -- (c-11-1) -- (c-111) -- cycle;

    \draw[very thick] (0,0,-1) -- (0,0,1) (0,-1,0) -- (0,1,0) (-1,0,0) -- (1,0,0);

    \filldraw[yellow,draw=black] (c111) -- (c1-11) -- (c-1-11) -- (c-111) -- cycle; 
    \filldraw[green,draw=black] (c-1-1-1) -- (c-1-11) -- (c-111) -- (c-11-1) -- cycle;
    \filldraw[orange,draw=black] (c-1-1-1) -- (c-1-11) -- (c1-11) -- (c1-1-1) -- cycle;
\end{scope}

\draw[fill=black,very thick] (0,-1,0) -- (0,-\dumbbelllength,0) circle (0.05cm);
\draw[fill=black,very thick] (-1,0,0) -- (-\dumbbelllength,0,0) circle (0.05cm);
\draw[fill=black,very thick] (0,0,1) -- (0,0,\dumbbelllength) circle (0.05cm);

\draw[thick] (-2,-2,-2) -- node[below right=1cm] {\huge x} (2,-2,-2);
\draw[thick] (-2,-2,-2) -- node[below left=1cm] {\huge y} (-2,2,-2);
\draw[thick] (-2,2,-2) -- node[left=1cm] {\huge z} (-2,2,2);

\foreach \c in {-2,...,2}
{   \draw (-2,2,\c) node[inner sep=0.05cm,fill=black,circle,label=\zangle+90:\c] {};
    \draw (-2,\c,-2) node[inner sep=0.05cm,fill=black,circle,label=\yangle+90:\c] {};
    \draw (\c,-2,-2) node[inner sep=0.05cm,fill=black,circle,label=\xangle-90:\c] {};
}

\end{tikzpicture}

\end{document}

Output

Answer 2

Perhaps you can use this tikz code as a starting point:

\documentclass{article}
\usepackage{tikz}
\usetikzlibrary{calc,3d}

\begin{document}

\begin{tikzpicture}[x  = {(-0.5cm,-0.5cm)},
                    y  = {(0.95cm,-0.25cm)},
                    z  = {(0cm,1cm)}]

\begin{scope}[canvas is yz plane at x=-1]
  \draw[blue] (-1,-1) -- (-1,1) -- (1,1) -- (1,-1) -- cycle ;
  \foreach \x in {-1,1}
    \foreach \y in {-1,1}
        \fill[blue] (\x,\y) circle (1pt);
\end{scope}
\begin{scope}[canvas is yz plane at x=1]
  \draw[blue] (-1,-1) -- (-1,1) -- (1,1) -- (1,-1) -- cycle;
    \foreach \x in {-1,1}
    \foreach \y in {-1,1}
        \fill[blue] (\x,\y) circle (1pt);
\end{scope}
\begin{scope}[canvas is xz plane at y=1]
  \draw[blue] (-1,-1) -- (-1,1) -- (1,1) -- (1,-1) -- cycle;
\end{scope}
\begin{scope}[canvas is xz plane at y=-1]
  \draw[blue] (-1,-1) -- (-1,1) -- (1,1) -- (1,-1) -- cycle;
\end{scope}
\begin{scope}[canvas is yz plane at x=0]
 \draw[red,dashed] (-1.5,0) -- (0,0) -- (1.5,0);
 \draw[red,dashed] (0,-1.5) -- (0,0) -- (0,1.5);
 \foreach \y in {-1.5,0,1.5} \fill[blue] (\y,0) circle (1pt);
 \foreach \z in {-1.5,1.5} \fill[blue] (0,\z) circle (1pt);
\end{scope}
\begin{scope}[canvas is xz plane at y=0]
\draw[red,dashed] (-1.5,0) -- (0,0) -- (1.5,0);
\foreach \x in {-1.5,1.5} \fill[blue] (\x,0) circle (1pt);
\end{scope}

\end{tikzpicture}

\end{document}

There remain many things to improve but it may get you on tracks. Also, there may be an easier solution with pgfplots.