\begin{tikzpicture}%
	[x={(0cm, 4cm)},
	y={(-5cm, 0cm)},
	z={(-2cm, 4cm)},
	scale=0.35,
	back/.style={loosely dotted, thin},
	edge/.style={color=blue!95!black, thick},
	facet/.style={fill=red!95!black,fill opacity=0.800000},
	vertex/.style={inner sep=1pt,circle,draw=green!25!black,fill=green!75!black,thick,anchor=base}]
\scriptsize

%%
%%
%% Coordinates of the vertices:
%% The name is given by the number of lattice points at heights 0,1,2,.... 
%% The label is given by the sequence of horizontal lengths of the path at heights 0,1,2,.... 
%% For instance: 
%%label 0003 is the path NNNEEE -> name 1114
%%label 1110 is the path ENENEN -> name 2221
%%label 0201 is the path NEENNE -> name 1312
%%
%%

\coordinate (c2311) at (0,-1,0);
\coordinate (c1411) at (1,-1,0);
%
\coordinate (c2221) at (0,0,0);
\coordinate (c1321) at (1,0,0);
\coordinate (c1231) at (2,1,0);
\coordinate (c1141) at (2,2,0);
\coordinate (c2131) at (0,2,0);
%
\coordinate (c2212) at (0,0,1);
\coordinate (c1312) at (1,0,1);
\coordinate (c1222) at (2,1,1);
\coordinate (c1132) at (2,2,1);
\coordinate (c2122) at (0,2,1);
%
\coordinate (c1213) at (3,2,1);
\coordinate (c1123) at (3,3,1);
\coordinate (c1114) at (3,4,1);
%
\coordinate (c2113) at (0,4,1);



% Drawing nodes
\node (n2311) at (c2311) {1200};
\node (n1411) at (c1411) {0300};
\node (n1321) at (c1321) {0210};
\node (n1312) at (c1312) {0201};
\node (n1222) at (c1222) {0111};
\node (n1213) at (c1213) {0102}; 
\node (n2221) at (c2221) {1110};
\node (n1231) at (c1231) {0120};
\node (n2212) at (c2212) {1101};
\node (n1132) at (c1132) {0021};
\node (n1123) at (c1123) {0012}; 
\node (n2131) at (c2131) {1020};
\node (n1141) at (c1141) {0030};
\node (n2122) at (c2122) {1011};
\node (n2113) at (c2113) {1002};
\node (n1114) at (c1114) {0003};


% Drawing edges in the front
% List of edges in the front
\def\listEdgesFront{
n2311/n1411, n1411/n1321, n2311/n2221,
n2221/n1321, n1321/n1231, n1231/n1141, n2221/n2131, n2131/n1141,
n1321/n1312, n1231/n1222, n1141/n1132, n2131/n2122,
n1312/n1222, n1222/n1132, n2122/n1132,
n1222/n1213, n1213/n1123, n1123/n1114, n2122/n2113, n2113/n1114, n1132/n1123}
;
%
%
\foreach \x/\y in \listEdgesFront{
%    \draw[edge] (\x) -- (\y);
    \draw[edge,->] (\x) -- (\y);
}

% Drawing edges in the back
% List of edges in the back
\def\listEdgesBack{
n2221/n2212,
n2212/n2122, n2212/n1312};
%
%
\foreach \x/\y in \listEdgesBack{
%    \draw[edge,back] (\x) -- (\y);
    \draw[edge,back,->] (\x) -- (\y);
}

\end{tikzpicture}