Package pgfplots error could not read table file in figure

Oh wow, that's a really cool figure! I think you have mixed up the syntax for plotting table data, you used the one for files. To "repair" your code I create the file, alternatively you could adjust the syntax.

\documentclass[test]{report}
\usepackage[T1]{fontenc}
\usepackage[latin9]{luainputenc}
\setcounter{secnumdepth}{3}
\setcounter{tocdepth}{3}

\makeatletter
\usepackage{bohr}
\usepackage{carbohydrates}
\usepackage{chemfig}
\usepackage{tikz}
\usepackage{pgfplots}

\pgfplotsset{compat=1.12}

\@ifundefined{showcaptionsetup}{}{%
 \PassOptionsToPackage{caption=false}{subfig}}
\usepackage{subfig}
\makeatother

\usepackage{filecontents}
\begin{filecontents*}{mytable.dat}
x y z 
10 -1 -1 
10 1 -1 
10 1 1 
10 -1 1 
10 -1 -1 
\end{filecontents*}

\usepackage{babel}
\begin{document}
\begin{figure}
\subfloat[]{\begin{tikzpicture}[     
declare function={squarex(\t) =         
    (\t < 0.25) ? 1 : (             
        (\t < 0.5) ? (1 - (\t-0.25) * 8) : (                 
            (\t < 0.75) ? -1 : (-1 + (\t - 0.75) * 8)         
    )     
;},     
declare function={squarey(\t) =         
    (\t < 0.25) ? (-1 + \t*8) : (             
        (\t < 0.5) ? 1 : (                 
            (\t < 0.75) ? (1 - (\t - 0.5) * 8) : -1         
    )     
;} 
] 
\begin{axis}[    
axis equal image,      
z buffer=sort,
hide axis,      
domain=0:1, y domain = 0:10, samples y = 25,     
ylabel =y, xlabel=x,     clip=false 
]
\addplot3 [     
z buffer=none, domain=0:330, samples y=1,     
ultra thick, black, -latex] (     
-0.5,     
{sin(x)*1.5},     {cos(x)*1.5} 
);
\addplot3 [surf, shader=flat, fill=black!10, draw=black] (     
y,     
{squarex(x) * cos(y*9) - squarey(x) * sin(y*9)},     
{squarex(x) * sin(y*9) + squarey(x) * cos(y*9)} 
);
\addplot3 [z buffer=auto, fill=black!30, draw=black] table {mytable.dat};
\addplot3 [     
z buffer=auto, domain=-60:270, samples y=1,     
ultra thick, black, latex-] (     
10.5,     
{sin(x)*1.5},     
{cos(x)*1.5} );
\draw [ultra thick,-latex] (3.5,0,2) -- (6.5,0,2);
\node[rotate=-12] (label) at (5,0,2.7) {wave motion};
\end{axis} 
\end{tikzpicture}

}\hfill{}\subfloat[]{Other figure goes here.}

\caption{Torsional wave. a) a cuboid figure undergoing torsional         distortion
b) the bending and bucking in this bridge is caused by torsional waves}
\end{figure}

\end{document}

Torbjørn scooped me in adding the alternative, so his answer or the following code yields the same output.

\documentclass[test]{report}
\usepackage[T1]{fontenc}
\usepackage[latin9]{luainputenc}
\setcounter{secnumdepth}{3}
\setcounter{tocdepth}{3}

\makeatletter
\usepackage{bohr}
\usepackage{carbohydrates}
\usepackage{chemfig}
\usepackage{tikz}
 \usepackage{pgfplots}

\pgfplotsset{compat=1.12}

\@ifundefined{showcaptionsetup}{}{%
 \PassOptionsToPackage{caption=false}{subfig}}
\usepackage{subfig}
\makeatother

\usepackage{babel}
\begin{document}
\begin{figure}
\subfloat[]{\begin{tikzpicture}[     
declare function={squarex(\t) =         
    (\t < 0.25) ? 1 : (             
        (\t < 0.5) ? (1 - (\t-0.25) * 8) : (                 
            (\t < 0.75) ? -1 : (-1 + (\t - 0.75) * 8)         
    )     
;},     
declare function={squarey(\t) =         
    (\t < 0.25) ? (-1 + \t*8) : (             
        (\t < 0.5) ? 1 : (                 
            (\t < 0.75) ? (1 - (\t - 0.5) * 8) : -1         
    )     
;} 
] 
\begin{axis}[    
axis equal image,      
z buffer=sort,
hide axis,      
domain=0:1, y domain = 0:10, samples y = 25,     
ylabel =y, xlabel=x,     clip=false 
]
\addplot3 [     
z buffer=none, domain=0:330, samples y=1,     
ultra thick, black, -latex] (     
-0.5,     
{sin(x)*1.5},     {cos(x)*1.5} 
);
\addplot3 [surf, shader=flat, fill=black!10, draw=black] (     
y,     
{squarex(x) * cos(y*9) - squarey(x) * sin(y*9)},     
{squarex(x) * sin(y*9) + squarey(x) * cos(y*9)} 
);
\addplot3 [z buffer=auto, fill=black!30, draw=black] table[row sep=crcr] { 
x y z \\
10 -1 -1\\ 
10 1 -1 \\
10 1 1 \\
10 -1 1 \\
10 -1 -1 \\
};
\addplot3 [     
z buffer=auto, domain=-60:270, samples y=1,     
ultra thick, black, latex-] (     
10.5,     
{sin(x)*1.5},     
{cos(x)*1.5} );
\draw [ultra thick,-latex] (3.5,0,2) -- (6.5,0,2);
\node[rotate=-12] (label) at (5,0,2.7) {wave motion};
\end{axis} 
\end{tikzpicture}

}\hfill{}\subfloat[]{Other figure goes here

}

\caption{Torsional wave. a) a cuboid figure undergoing torsional         distortion
b) the bending and bucking in this bridge is caused by torsional waves}
\end{figure}

\end{document}

With table[row sep=\\] and a \\ at the end of each line it works (at least for me).

\documentclass[test]{report}
\usepackage[T1]{fontenc}
\usepackage[latin9]{luainputenc}
\setcounter{secnumdepth}{3}
\setcounter{tocdepth}{3}

\makeatletter
\usepackage{bohr}
\usepackage{carbohydrates}
\usepackage{chemfig}
\usepackage{tikz}
 \usepackage{pgfplots}

\pgfplotsset{compat=1.12}

\@ifundefined{showcaptionsetup}{}{%
 \PassOptionsToPackage{caption=false}{subfig}}
\usepackage{subfig}
\makeatother

\usepackage{babel}
\begin{document}
\begin{figure}
\subfloat[]{\begin{tikzpicture}[     
declare function={squarex(\t) =         
    (\t < 0.25) ? 1 : (             
        (\t < 0.5) ? (1 - (\t-0.25) * 8) : (                 
            (\t < 0.75) ? -1 : (-1 + (\t - 0.75) * 8)         
    )     
;},     
declare function={squarey(\t) =         
    (\t < 0.25) ? (-1 + \t*8) : (             
        (\t < 0.5) ? 1 : (                 
            (\t < 0.75) ? (1 - (\t - 0.5) * 8) : -1         
    )     
;} 
] 
\begin{axis}[    
axis equal image,      
z buffer=sort,
hide axis,      
domain=0:1, y domain = 0:10, samples y = 25,     
ylabel =y, xlabel=x,     clip=false 
]
\addplot3 [     
z buffer=none, domain=0:330, samples y=1,     
ultra thick, black, -latex] (     
-0.5,     
{sin(x)*1.5},     {cos(x)*1.5} 
);
\addplot3 [surf, shader=flat, fill=black!10, draw=black] (     
y,     
{squarex(x) * cos(y*9) - squarey(x) * sin(y*9)},     
{squarex(x) * sin(y*9) + squarey(x) * cos(y*9)} 
);
\addplot3 [z buffer=auto, fill=black!30, draw=black] table[row sep=\\] {%
x y z \\
10 -1 -1\\ 
10 1 -1 \\
10 1 1 \\
10 -1 1 \\
10 -1 -1 \\
};
\addplot3 [     
z buffer=auto, domain=-60:270, samples y=1,     
ultra thick, black, latex-] (     
10.5,     
{sin(x)*1.5},     
{cos(x)*1.5} );
\draw [ultra thick,-latex] (3.5,0,2) -- (6.5,0,2);
\node[rotate=-12] (label) at (5,0,2.7) {wave motion};
\end{axis} 
\end{tikzpicture}

}\hfill{}\subfloat[]{Other figure goes here

}

\caption{Torsional wave. a) a cuboid figure undergoing torsional         distortion
b) the bending and bucking in this bridge is caused by torsional waves}
\end{figure}

\end{document}