

\begin{tikzpicture}%
	[x={(240:2cm)},
	y={(0:2cm)},
	z={(120:2cm)},
    scale=0.4]

\node (123) at (1,2,3) {123};
\node (213) at (2,1,3) {213};
\node (312) at (3,1,2) {312};
\node (321) at (3,2,1) {321};
\node (231) at (2,3,1) {231};
\node (132) at (1,3,2) {132};
\node (042) at (0,4,2) {042};
\node (-143) at (-1,4,3) {$\overline{1}43$};
\node (-134) at (-1,3,4) {$\overline{1}34$};
\node (024) at (0,2,4) {024};
\node (015) at (0,1,5) {015};
\node (105) at (1,0,5) {105};
\node (204) at (2,0,4) {204};
\node (402) at (4,0,2) {402};
\node (4-13) at (4,-1,3) {$4\overline{1}3$};
\node (3-14) at (3,-1,4) {$3\overline{1}4$};
\node (5-23) at (5,-2,3) {$5\overline{2}3$};
\node (6-22) at (6,-2,2) {$6\overline{2}2$};
\node (501) at (5,0,1) {501};
\node (6-11) at (6,-1,1) {$6\overline{1}1$};

\draw (123) -- (024) -- (015) -- (105) -- (204) -- (213);
\draw (123) -- (132) -- (042) -- (-143) -- (-134) -- (024);
\draw (123) -- (213) -- (312) -- (321) -- (231) -- (132);
\draw (312) -- (402) -- (4-13) -- (5-23) -- (6-22);
\draw (213) -- (204) -- (3-14) -- (4-13) -- (5-23) -- (6-22);
\draw (402) -- (501) -- (6-11) -- (6-22);

%drawn from top right to bottom left
\draw[purple] (-3/3,11/3,10/3) -- (-1/3,8/3,11/3) -- (10/3,1/3,7/3) -- (14/3,-4/3,8/3) -- (17/3,-6/3,7/3);
\draw[bluishgreen] (-2/3,12/3,8/3) -- (1/3,10/3,7/3) -- (5/3,5/3,8/3) -- (16/3,-2/3,4/3) -- (18/3,-9/6,9/6) ;
\draw[skyblue] (-3/6,15/6,12/3) -- (4/3,4/3,10/3) -- (8/3,-1/3,11/3) -- (16/3,-6/3,8/3);

\draw[orange](0,3,3) circle (2/3); 
\draw[orange](5,-1,2) circle (2/3); 
\draw[red](0,0,0) circle (2/3); 
\draw[blue](-3,-3,0) circle (2/3); 
\end{tikzpicture}  
            