mjhjmtu

During the current review of the tensors I have arrived at a page of Wikipedia where you can see the symbol of Levi-Civita in a beautiful three-dimensional matrix.

I hope that nobody will be angry with me if I do not produce any MWE but for me it would be nice to see the construction of a matrix so made and can be made available to other users.

More or less:

documentclass[tikz,border=2mm]standalone 
usetikzlibrarypositioning, matrix
usepackageamsmath

newcommandarrayfilling[2]
fill[#2!30, opacity=.5] ([shift=(1mm,1mm)]#1.north west) coordinate(#1auxnw)--([shift=(1mm,1mm)]#1.north east)coordinate(#1auxne) to[out=-75, in=75] ([shift=(1mm,-1mm)]#1.south east)coordinate(#1auxse)--([shift=(1mm,-1mm)]#1.south west)coordinate(#1auxsw) to[out=105, in=-105] cycle;
fill[#2!80!black, opacity=1] (#1auxne) to[out=-75, in=75] (#1auxse) to[out=78, in=-78] cycle;
fill[#2!80!black, opacity=1] (#1auxnw) to[out=-105, in=105] (#1auxsw) to[out=102, in=-102] cycle;



begindocument
begintikzpicture[font=ttfamily,
 mymatrix/.style=
 matrix of math nodes, inner sep=0pt, color=#1,
 column sep=-pgflinewidth, row sep=-pgflinewidth, anchor=south west, 
 nodes=anchor=center, minimum width=5mm, 
 minimum height=3mm, outer sep=0pt, inner sep=0pt, 
 text width=5mm, align=right,
 draw=none, font=small,

]

matrix (C) [mymatrix=green] at (6mm,5mm) 
0 & 1 & 0 \ -1 & 0 & 0\ 0 & 0 & 0\;
arrayfillingCgreen

matrix (B) [mymatrix=red] at (3mm,2.5mm)
0 & 0 & -1 \ 0 & 0 & 0\ 1 & 0 & 0\;
arrayfillingBred

matrix (A) [mymatrix=blue] at (0,0)
0 & 0 & 0 \ 0 & 0 & 1\ 0 & -1 & 0\;
arrayfillingAblue

foreach i in auxnw, auxne, auxse, auxsw
draw[brown, ultra thin] (Ai)--(Ci);

node[below left=-1mm and 5mm of B.west] $epsilon_ijk =$;
endtikzpicture
enddocument

Something like that?

documentclass[tikz,border=3.14mm]standalone
usepackagemathtools
usetikzlibrarymatrix,backgrounds,3d
usepackagetikz-3dplot
%definecolormygreenRGB12,252,12
begindocument
tdplotsetmaincoords7520
begintikzpicture[tdplot_main_coords]
 beginscope[canvas is xz plane at y=1,transform shape]
 node[inner sep=0pt,text=green!70!black,opacity=0.8] (mat1)
 $displaystylebeginpmatrix*[r]
 0 & 1 & 0 \
 -1 & 0 & 0 \
 0 & 0 & 0 \
 endpmatrix*$;
 beginscope[on background layer]
 fill[green!70!black,opacity=0.2] ([xshift=8.5pt]mat1.south west) 
 coordinate (blb) to[out=140,in=-140,looseness=0.7]
 ([xshift=8.5pt]mat1.north west) coordinate (tlb) -- 
 ([xshift=-8.5pt]mat1.north east) coordinate (trb)
 to[out=-40,in=40,looseness=0.7] ([xshift=-8.5pt]mat1.south east)
 coordinate (brb)
 -- cycle;
 endscope 
 endscope
 %
 beginscope[canvas is xz plane at y=0,transform shape]
 node[inner sep=0pt,text=red,opacity=0.8] (mat2) $displaystyle
 beginpmatrix*[r]
 0 & 0 & -1 \
 0 & 0 & 0 \
 1 & 0 & 0 \
 endpmatrix*$;
 beginscope[on background layer]
 fill[red,opacity=0.2] ([xshift=8.5pt]mat2.south west) to[out=140,in=-140,looseness=0.7]
 ([xshift=8.5pt]mat2.north west) -- ([xshift=-8.5pt]mat2.north east) 
 to[out=-40,in=40,looseness=0.7] ([xshift=-8.5pt]mat2.south east) -- cycle;
 endscope 
 endscope
 %
 beginscope[canvas is xz plane at y=-1,transform shape]
 node[inner sep=0pt,text=blue,opacity=0.8] (mat3) $displaystyle
 beginpmatrix*[r]
 0 & 0 & 0 \
 0 & 0 & 1 \
 0 & -1 & 0 \
 endpmatrix*$;
 beginscope[on background layer]
 fill[blue,opacity=0.2]
 ([xshift=8.5pt]mat3.south west) coordinate (blf)
 to[out=140,in=-140,looseness=0.7]
 ([xshift=8.5pt]mat3.north west) coordinate (tlf) 
 -- ([xshift=-8.5pt]mat3.north east) coordinate (trf)
 to[out=-40,in=40,looseness=0.7] ([xshift=-8.5pt]mat3.south east) 
 coordinate (brf) -- cycle;
 endscope 
 endscope
 foreach X in tl,tr,br
 draw[thin,orange] (X f) -- (X b);
 beginscope[on background layer]
 draw[thin,orange] (blf) -- (blb);
 endscope
node[left] at (mat3.west) $varepsilon_ijk=$;
endtikzpicture
enddocument

EDIT: Aligned the entries right, big thanks to Barbara Beeton. (I just wonder why no one complained that the Levi-Civita tensor is not a tensor, but a tensor density. ;-)

2nd EDIT: Response to Anush's comment (well-taken! ;-).

documentclass[tikz,border=3.14mm]standalone
usepackagemathtools
usetikzlibrarymatrix,backgrounds,3d
usepackagetikz-3dplot
begindocument
tdplotsetmaincoords7520
begintikzpicture[tdplot_main_coords]
 beginscope[canvas is xz plane at y=1,transform shape]
 node[inner sep=0pt,text=green!70!black,opacity=0.8] (mat1)
 $displaystylebeginpmatrix*[r]
 0 & hphantom-1 & hphantom-0 \
 -1 & 0 & 0 \
 0 & 0 & 0 \
 endpmatrix*$;
 beginscope[on background layer]
 fill[green!70!black,opacity=0.2] ([xshift=8.5pt]mat1.south west) 
 coordinate (blb) to[out=140,in=-140,looseness=0.7]
 ([xshift=8.5pt]mat1.north west) coordinate (tlb) -- 
 ([xshift=-8.5pt]mat1.north east) coordinate (trb)
 to[out=-40,in=40,looseness=0.7] ([xshift=-8.5pt]mat1.south east)
 coordinate (brb)
 -- cycle;
 endscope 
 endscope
 %
 beginscope[canvas is xz plane at y=0,transform shape]
 node[inner sep=0pt,text=red,opacity=0.8] (mat2) $displaystyle
 beginpmatrix*[r]
 hphantom-0 & hphantom-0 & -1 \
 0 & 0 & 0 \
 1 & 0 & 0 \
 endpmatrix*$;
 beginscope[on background layer]
 fill[red,opacity=0.2] ([xshift=8.5pt]mat2.south west) to[out=140,in=-140,looseness=0.7]
 ([xshift=8.5pt]mat2.north west) -- ([xshift=-8.5pt]mat2.north east) 
 to[out=-40,in=40,looseness=0.7] ([xshift=-8.5pt]mat2.south east) -- cycle;
 endscope 
 endscope
 %
 beginscope[canvas is xz plane at y=-1,transform shape]
 node[inner sep=0pt,text=blue,opacity=0.8] (mat3) $displaystyle
 beginpmatrix*[r]
 hphantom-0 & 0 & hphantom-0 \
 0 & 0 & 1 \
 0 & -1 & 0 \
 endpmatrix*$;
 beginscope[on background layer]
 fill[blue,opacity=0.2]
 ([xshift=8.5pt]mat3.south west) coordinate (blf)
 to[out=140,in=-140,looseness=0.7]
 ([xshift=8.5pt]mat3.north west) coordinate (tlf) 
 -- ([xshift=-8.5pt]mat3.north east) coordinate (trf)
 to[out=-40,in=40,looseness=0.7] ([xshift=-8.5pt]mat3.south east) 
 coordinate (brf) -- cycle;
 endscope 
 endscope
 foreach X in tl,tr,br
 draw[thin,orange] (X f) -- (X b);
 beginscope[on background layer]
 draw[thin,orange] (blf) -- (blb);
 endscope
 beginscope[canvas is xz plane at y=0,transform shape]
 node[left] at (mat2.west -| mat3.west) $varepsilon_ijk=$;
 endscope
endtikzpicture
enddocument