Issues after making a cuboid in tikz

Question

I'm looking to make a rectangular prism that has color shading, with red at the bottom of the entire prism and blue at the top. So I adapted the following code from here

\documentclass{report}
\usepackage{tikz}
\usetikzlibrary{3d}
\begin{tikzpicture}[x  = {(2cm,1.5cm)},
y  = {(5.75cm,0cm)},
z  = {(0cm,3cm)}]
\begin{scope}[canvas is yz plane at x=-1]
\shade[bottom color = red!50, top color = blue!50] (-1,-1) rectangle (1,1);
\end{scope}
\begin{scope}[canvas is xz plane at y = 1]
\shade[bottom color = red!50, top color = blue!50] (-1,-1) rectangle (1,1);
\end{scope}
\begin{scope}[canvas is yx plane at z = 1]
\fill[blue!50] (-1,-1) rectangle (1,1);
\end{scope}
\end{tikzpicture}

which yields

Now, there are some issues with the above picture that I was hoping someone could help me with.

1. The first is that the left and right edges of the top (lid) of the prism aren't parallel, and changing the dimensions in the tikz picture never fixes this. Why is this and how can it be fixed?
2. I actually want the shading to be red along the entire bottom of the prism and blue along the entire top. The colouring on front face and the top are both fine. However, the side face has red in the top left corner of the face, when it should be blue to match the colour on the top. I played around with the shadings but to no avail, so I was wondering if this was fixable too?
3. I was hoping to bold the edges of the prism to outline where each face begins and ends, though I am having trouble finding code that works with what I have already done.
4. Finally, is it possible to get the 'hidden' edges put in the back of the cuboid? By hidden, I mean those three edges from the back face that meet the bottom and top of the prism.

Sorry for the many questions, I'm not very competent with tikz yet. Thanks in advance.

EDIT:

Thanks to the responses below. I managed to get the hidden sides on the picture, as well as the colouring on the bottom of the side face correct. However, the colouring at the top of the side face isn't correct, it is too red and doesn't match the colour of the top face (lid) of the cuboid. Here is the code

\begin{tikzpicture}[join = round, xscale = 12, yscale = 6]

\colorlet{bcolor}{red!60}   
\colorlet{tcolor}{blue!100}
\colorlet{ttcolor}{blue!100}

\shadedraw[bottom color = bcolor, top color = tcolor]
(-1,-1) coordinate (A) rectangle (0,0);     
\shadedraw[xscale = 0.5, yslant = 0.5, bottom color = bcolor, top color = tcolor, shading angle = 25]
(0,-1) rectangle (1,0) 
(1,-1) coordinate (B)
(-1,0) coordinate (O);      
\draw[yscale = 0.5, xslant = 0.5, fill = ttcolor] (-1,0) rectangle (0,1) (-1,1) coordinate (C);

\draw[dashed, opacity = 0.7] (O)--(A) (O)--(B) (O)--(C);
\end{tikzpicture}   

which gives

The shade at the top of the side face (touching the lid of the cuboid) should be a darker blue, to match the colour of the lid.

Answer 1

You can transform shadings. However, this requires you to resort to transform canvas, which is a bit "violent". The lower level command corresponding to transform canvas is \pgflowlevelsynccm. This is an untuned version with an orthographic projections.

\documentclass[tikz,border=3mm]{standalone}
\usepackage{tikz-3dplot}
\begin{document}
\tdplotsetmaincoords{70}{110}
\begin{tikzpicture}[tdplot_main_coords,line cap=round,line join=round,
    fill opacity=0.8,scale=2]
 \path foreach \X in {-1,1} {foreach \Y in {-1,1} 
 {foreach \Z in {-1,1} {(\X,\Y,\Z) coordinate (p\X\Y\Z)}}};
 \draw[dashed] (p-11-1) -- (p-1-1-1) edge (p-1-11) -- (p1-1-1);
 \begin{scope}[canvas is xz plane at y=1]
  \pgflowlevelsynccm
  \draw[bottom color = red, top color = blue]  (-1,-1) rectangle (1,1);
 \end{scope}
 \begin{scope}[canvas is yz plane at x=1]
  \pgflowlevelsynccm
  \draw[bottom color = red, top color = blue]  (-1,-1) rectangle (1,1);
 \end{scope}
 \begin{scope}[canvas is xy plane at z=1]
  \draw[fill=blue]  (-1,-1) rectangle (1,1);
 \end{scope}
\end{tikzpicture}
\end{document}

OLDER VERSIONS:

\documentclass[tikz,border=3mm]{standalone} 
\usetikzlibrary{3d}
\begin{document}
\begin{tikzpicture}[x  = {(2cm,1.5cm)},
    y  = {(5.75cm,0cm)},
    z  = {(0cm,3cm)}]
  \begin{scope}[canvas is yz plane at x=-1]
   \shade[bottom color = red!50, top color = blue!50] (-1,-1) rectangle (1,1);
  \end{scope}
  \begin{scope}
   \clip[canvas is xz plane at y = 1] (-1,-1) rectangle (1,1);
   \shade[transform canvas={canvas is xz plane at y = 1},
     bottom color = red!50, top color = blue!50] (-1,-1) rectangle (1,1);
  \end{scope}
  \begin{scope}[canvas is yx plane at z = 1]
   \fill[blue!50] (-1,-1) rectangle (1,1);
  \end{scope}
\end{tikzpicture}
\end{document}

In this version the color spectrum is not quite correct, as you noted, since parts are clipped away.

Here is a second version which is free of that problem, but very tuned. There are two reasons for the tuning: transform canvas is violent and the 3d projection is non-orthographic, so I did not find a good way to invert it. However, this (admittedly tuned and hence ugly coded) version substantiates once more that one can use canvas transformations to transform shadings.

\documentclass[tikz,border=3mm]{standalone} 
\usetikzlibrary{3d,calc}
\begin{document}
\begin{tikzpicture}[x  = {(2cm,1.5cm)},
    y  = {(5.75cm,0cm)},
    z  = {(0cm,3cm)}]
  \begin{scope}[canvas is yz plane at x=-1]
   \shade[bottom color = red!50, top color = blue!50] (-1,-1) rectangle (1,1);
  \end{scope}
  \begin{scope}
   \path [canvas is xz plane at y = 1] (0,0) coordinate (BL) (0,1) coordinate (TL)
    (1,0) coordinate (BR) (1,1) coordinate (TR);
   \path  let \p1=($(BR)-(BL)$) in  
   [canvas is xz plane at y = 1,yslant={-2*\y1/\x1/3},yshift=6.5pt]
   (-1,-1) coordinate (BL') (-1,1) coordinate (TL')
    (1,-1) coordinate (BR') (1,1) coordinate (TR');
   \shade let \p1=($(BR)-(BL)$) in
   [transform canvas={yslant={\y1/\x1},yshift=-5cm},
     bottom color = red!50, top color = blue!50] 
     (BL') -- (BR') -- (TR') -- (TL') -- cycle;
  \end{scope}
  \begin{scope}[canvas is yx plane at z = 1]
   \fill[blue!50] (-1,-1) rectangle (1,1);
  \end{scope}
\end{tikzpicture}
\end{document}

Or with some lines.

\documentclass[tikz,border=3mm]{standalone} 
\usetikzlibrary{3d,calc}
\begin{document}
\begin{tikzpicture}[x  = {(2cm,1.5cm)},
    y  = {(5.75cm,0cm)},
    z  = {(0cm,3cm)},fill opacity=0.7,line cap=round,line join=round]
  \begin{scope}[canvas is yz plane at x=1]
   \draw[dashed]  (1,-1) -- (-1,-1) coordinate (B) -- (-1,1);
  \end{scope}
   \draw [dashed] (-1,-1,-1) -- (B);
  \begin{scope}
   \path [canvas is xz plane at y = 1] (0,0) coordinate (BL) (0,1) coordinate (TL)
    (1,0) coordinate (BR) (1,1) coordinate (TR);
   \path  let \p1=($(BR)-(BL)$) in  
   [canvas is xz plane at y = 1,yslant={-2*\y1/\x1/3},yshift=6.5pt]
   (-1,-1) coordinate (BL') (-1,1) coordinate (TL')
    (1,-1) coordinate (BR') (1,1) coordinate (TR');
   \shade let \p1=($(BR)-(BL)$) in
   [transform canvas={yslant={\y1/\x1},yshift=-5cm},
     bottom color = red!50, top color = blue!50] 
     (BL') -- (BR') -- (TR') -- (TL') -- cycle;
  \end{scope}
  \begin{scope}[canvas is yz plane at x=-1]
   \draw[bottom color = red!50, top color = blue!50] (-1,-1) rectangle (1,1);
  \end{scope}
  \begin{scope}[canvas is yx plane at z = 1]
   \draw[fill=blue!50] (-1,-1) rectangle (1,1);
  \end{scope}
  \draw (TR) -- (1,1,-1) -- (-1,1,-1);
\end{tikzpicture}
\end{document}

Answer 2

How about this? I use plain TikZ to play around with geometric transformations, and add another color for the top of the cuboid.

\documentclass[tikz,border=5mm]{standalone}
\begin{document}
\begin{tikzpicture}
\colorlet{bcolor}{red!50}   
\colorlet{tcolor}{blue!50}
\colorlet{ttcolor}{blue!55}

\shade[bottom color=bcolor,top color =tcolor] (-1,-1) rectangle (0,0);      
\shade[xscale=.5,yslant=.5,bottom color=bcolor,top color=tcolor] (0,-1) rectangle (1,0);        
\fill[yscale=.5,xslant=.5,ttcolor] (-1,0) rectangle (0,1);
\end{tikzpicture}   
\end{document}  

For hidden lines, you can attach necessary points under action of the above geometric transformation, and use opacity. I add middle color as OP's request.

\documentclass[tikz,border=5mm]{standalone}
\begin{document}
\begin{tikzpicture}[join=round,scale=2]
\colorlet{tcolor}{blue}   
\colorlet{bcolor}{red}
\colorlet{mcolor}{bcolor!50!tcolor}

\shadedraw[bottom color=bcolor,middle color=mcolor,top color =tcolor]
(-1,-1) coordinate (A) rectangle (0,0);     
\shadedraw[xscale=.5,yslant=.5,bottom color=bcolor,middle color=mcolor,top color=tcolor]
(0,-1) rectangle (1,0) 
(1,-1) coordinate (B)
(-1,0) coordinate (O);      
\draw[yscale=.5,xslant=.5,fill=tcolor] (-1,0) rectangle (0,1) (-1,1) coordinate (C);

\draw[dashed,opacity=.5] (O)--(A) (O)--(B) (O)--(C);
\end{tikzpicture}   
\end{document}

Note that these are still 3D-like effect. You may use Asymptote to get more real-3D-feeling figure.