Use tikz folding library to create a candy or popcorn style box

Question

How can I use a tikz folding library to create a box that does not have regular faces?. For instance, consider this sketch:

I need first to create a trapezoid face to use it with the folding library. This is my first attempt:

\documentclass[11pt]{article}
\usepackage{tikz}
\usetikzlibrary{folding}

\makeatletter 

\def\tikz@lib@fold@trapecio#1#2#3#4#5{%
  \begin{scope}[xshift=.5\tikz@lib@fold@length,yshift=.5\tikz@lib@fold@length]
    #1
  \end{scope}
  \begin{scope}[yshift=0.8\tikz@lib@fold@length,rotate=20]
    #2 
    \node{Edge A};
  \end{scope}
  \begin{scope}[xshift=\tikz@lib@fold@length,yshift=\tikz@lib@fold@length,rotate=-90]
    #3
    \node{Edge B};
  \end{scope}
  \begin{scope}[xshift=\tikz@lib@fold@length,rotate=180]
    #4
    \node{Edge C};
  \end{scope}
  \begin{scope}[rotate=90]
    #5
    \node{Edge D};
  \end{scope}
}

\def\tikzfoldingtetrahedron#1[#2]#3;{%
  \begingroup%
    \tikzset{#2}%
    \tikz@lib@fold@trapecio
        {\tikz@lib@fold@face@A}
        {\tikz@lib@fold@path}
        {\tikz@lib@fold@path}
        {\tikz@lib@fold@path}
        {\tikz@lib@fold@path}
  \endgroup
}
\makeatother


\begin{document}
  \begin{tikzpicture}[scale=1]
  \path pic [
    folding line length=4cm,
    transform shape,
    numbered faces
  ]
  {tetrahedron folding};
  \end{tikzpicture}
\end{document} 

Please, ignore the tetrahedron name, I didn't realize how to define a new folding name. The code gives this picture:

How can I fix the connecting lines between the edges? Even if I compute the proper angles, I need two or more different folding lengths. In all the folding library examples I have seen, there is only one folding length.