
    \begin{tabular}{cc}

\begin{tikzpicture}[scale=0.2]
    %tikz doesn't support 4d coordinate systems. So I pieced it together with this
    \node[coordinate] (p1) at (1,0){};
    \node[coordinate] (p2) at (0,1){};
    \node[coordinate] (p3) at (-0.4,-0.2){};
    \node[coordinate] (x1) at ($(p1)+(p2)+(p3)$){};
    \node[coordinate] (x2) at ($(p1)-(p2)-(p3)$){};
    \node[coordinate] (x3) at ($(p3)-(p1)-(p2)$){};
    \node[coordinate] (x4) at ($(p2)-(p1)-(p3)$){};

    
    %w1: 1,-3,1,1
    %w2: 1,1,-3,1
    %w3: 1,1,1,-3
    %w4: -3,1,1,1
    
    %(w1) at ($3.5*(x1)+-0.5*(x2)+3.5*(x3)+3.5*(x4)$) {w1};
    %(w2) at ($3.5*(x1)+3.5*(x2)+-0.5*(x3)+3.5*(x4)$) {w2};
    %(w3) at ($3.5*(x1)+3.5*(x2)+3.5*(x3)+-0.5*(x4)$) {w3};
    %(w4) at ($-0.5*(x1)+3.5*(x2)+3.5*(x3)+3.5*(x4)$) {w4};

\node[coordinate] (1234) at ($1*(x1)+2*(x2)+3*(x3)+4*(x4)$) {};
\node[coordinate] (2134) at ($2*(x1)+1*(x2)+3*(x3)+4*(x4)$) {};
\node[coordinate] (0235) at ($0*(x1)+2*(x2)+3*(x3)+5*(x4)$) {};
\node[coordinate] (1324) at ($1*(x1)+3*(x2)+2*(x3)+4*(x4)$) {};
\node[coordinate] (1243) at ($1*(x1)+2*(x2)+4*(x3)+3*(x4)$) {};
\node[coordinate] (3124) at ($3*(x1)+1*(x2)+2*(x3)+4*(x4)$) {};
\node[coordinate] (2035) at ($2*(x1)+0*(x2)+3*(x3)+5*(x4)$) {};
\node[coordinate] (2143) at ($2*(x1)+1*(x2)+4*(x3)+3*(x4)$) {};
\node[coordinate] (-1245) at ($-1*(x1)+2*(x2)+4*(x3)+5*(x4)$) {};
\node[coordinate] (0325) at ($0*(x1)+3*(x2)+2*(x3)+5*(x4)$) {};
\node[coordinate] (0136) at ($0*(x1)+1*(x2)+3*(x3)+6*(x4)$) {};
\node[coordinate] (2314) at ($2*(x1)+3*(x2)+1*(x3)+4*(x4)$) {};
\node[coordinate] (1423) at ($1*(x1)+4*(x2)+2*(x3)+3*(x4)$) {};
\node[coordinate] (0253) at ($0*(x1)+2*(x2)+5*(x3)+3*(x4)$) {};
\node[coordinate] (1342) at ($1*(x1)+3*(x2)+4*(x3)+2*(x4)$) {};
\node[coordinate] (4123) at ($4*(x1)+1*(x2)+2*(x3)+3*(x4)$) {};
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\node[coordinate] (3025) at ($3*(x1)+0*(x2)+2*(x3)+5*(x4)$) {};
\node[coordinate] (1036) at ($1*(x1)+0*(x2)+3*(x3)+6*(x4)$) {};
\node[coordinate] (2-145) at ($2*(x1)+-1*(x2)+4*(x3)+5*(x4)$) {};
\node[coordinate] (3142) at ($3*(x1)+1*(x2)+4*(x3)+2*(x4)$) {};
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\node[coordinate] (-1425) at ($-1*(x1)+4*(x2)+2*(x3)+5*(x4)$) {};
\node[coordinate] (0316) at ($0*(x1)+3*(x2)+1*(x3)+6*(x4)$) {};
\node[coordinate] (0127) at ($0*(x1)+1*(x2)+2*(x3)+7*(x4)$) {};
\node[coordinate] (2413) at ($2*(x1)+4*(x2)+1*(x3)+3*(x4)$) {};
\node[coordinate] (2305) at ($2*(x1)+3*(x2)+0*(x3)+5*(x4)$) {};
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\node[coordinate] (2341) at ($2*(x1)+3*(x2)+4*(x3)+1*(x4)$) {};
\node[coordinate] (5023) at ($5*(x1)+0*(x2)+2*(x3)+3*(x4)$) {};
\node[coordinate] (4213) at ($4*(x1)+2*(x2)+1*(x3)+3*(x4)$) {};
\node[coordinate] (4132) at ($4*(x1)+1*(x2)+3*(x3)+2*(x4)$) {};
\node[coordinate] (3205) at ($3*(x1)+2*(x2)+0*(x3)+5*(x4)$) {};
\node[coordinate] (4-125) at ($4*(x1)+-1*(x2)+2*(x3)+5*(x4)$) {};
\node[coordinate] (3016) at ($3*(x1)+0*(x2)+1*(x3)+6*(x4)$) {};
\node[coordinate] (1-146) at ($1*(x1)+-1*(x2)+4*(x3)+6*(x4)$) {};
\node[coordinate] (1027) at ($1*(x1)+0*(x2)+2*(x3)+7*(x4)$) {};
\node[coordinate] (3-245) at ($3*(x1)+-2*(x2)+4*(x3)+5*(x4)$) {};
\node[coordinate] (2-154) at ($2*(x1)+-1*(x2)+5*(x3)+4*(x4)$) {};
\node[coordinate] (3052) at ($3*(x1)+0*(x2)+5*(x3)+2*(x4)$) {};
\node[coordinate] (3241) at ($3*(x1)+2*(x2)+4*(x3)+1*(x4)$) {};
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\node[coordinate] (-2354) at ($-2*(x1)+3*(x2)+5*(x3)+4*(x4)$) {};
\node[coordinate] (-1056) at ($-1*(x1)+0*(x2)+5*(x3)+6*(x4)$) {};
\node[coordinate] (-1164) at ($-1*(x1)+1*(x2)+6*(x3)+4*(x4)$) {};
\node[coordinate] (-1524) at ($-1*(x1)+5*(x2)+2*(x3)+4*(x4)$) {};
\node[coordinate] (-1416) at ($-1*(x1)+4*(x2)+1*(x3)+6*(x4)$) {};
\node[coordinate] (1306) at ($1*(x1)+3*(x2)+0*(x3)+6*(x4)$) {};
\node[coordinate] (0217) at ($0*(x1)+2*(x2)+1*(x3)+7*(x4)$) {};
\node[coordinate] (3412) at ($3*(x1)+4*(x2)+1*(x3)+2*(x4)$) {};
\node[coordinate] (2503) at ($2*(x1)+5*(x2)+0*(x3)+3*(x4)$) {};
\node[coordinate] (24-15) at ($2*(x1)+4*(x2)+-1*(x3)+5*(x4)$) {};
\node[coordinate] (0613) at ($0*(x1)+6*(x2)+1*(x3)+3*(x4)$) {};
\node[coordinate] (0532) at ($0*(x1)+5*(x2)+3*(x3)+2*(x4)$) {};
\node[coordinate] (2431) at ($2*(x1)+4*(x2)+3*(x3)+1*(x4)$) {};
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\node[coordinate] (0361) at ($0*(x1)+3*(x2)+6*(x3)+1*(x4)$) {};
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\node[coordinate] (6013) at ($6*(x1)+0*(x2)+1*(x3)+3*(x4)$) {};
\node[coordinate] (5-124) at ($5*(x1)+-1*(x2)+2*(x3)+4*(x4)$) {};
\node[coordinate] (5032) at ($5*(x1)+0*(x2)+3*(x3)+2*(x4)$) {};
\node[coordinate] (5203) at ($5*(x1)+2*(x2)+0*(x3)+3*(x4)$) {};
\node[coordinate] (4312) at ($4*(x1)+3*(x2)+1*(x3)+2*(x4)$) {};
\node[coordinate] (4231) at ($4*(x1)+2*(x2)+3*(x3)+1*(x4)$) {};
\node[coordinate] (42-15) at ($4*(x1)+2*(x2)+-1*(x3)+5*(x4)$) {};
\node[coordinate] (3106) at ($3*(x1)+1*(x2)+0*(x3)+6*(x4)$) {};
\node[coordinate] (4-235) at ($4*(x1)+-2*(x2)+3*(x3)+5*(x4)$) {};
\node[coordinate] (4-116) at ($4*(x1)+-1*(x2)+1*(x3)+6*(x4)$) {};
\node[coordinate] (2017) at ($2*(x1)+0*(x2)+1*(x3)+7*(x4)$) {};
\node[coordinate] (0-156) at ($0*(x1)+-1*(x2)+5*(x3)+6*(x4)$) {};
\node[coordinate] (3-254) at ($3*(x1)+-2*(x2)+5*(x3)+4*(x4)$) {};
\node[coordinate] (1-164) at ($1*(x1)+-1*(x2)+6*(x3)+4*(x4)$) {};
\node[coordinate] (4-152) at ($4*(x1)+-1*(x2)+5*(x3)+2*(x4)$) {};
\node[coordinate] (3061) at ($3*(x1)+0*(x2)+6*(x3)+1*(x4)$) {};
\node[coordinate] (3250) at ($3*(x1)+2*(x2)+5*(x3)+0*(x4)$) {};
\node[coordinate] (1072) at ($1*(x1)+0*(x2)+7*(x3)+2*(x4)$) {};
\node[coordinate] (-2534) at ($-2*(x1)+5*(x2)+3*(x3)+4*(x4)$) {};
\node[coordinate] (-2453) at ($-2*(x1)+4*(x2)+5*(x3)+3*(x4)$) {};
\node[coordinate] (-1065) at ($-1*(x1)+0*(x2)+6*(x3)+5*(x4)$) {};
\node[coordinate] (-1614) at ($-1*(x1)+6*(x2)+1*(x3)+4*(x4)$) {};
\node[coordinate] (-1506) at ($-1*(x1)+5*(x2)+0*(x3)+6*(x4)$) {};
\node[coordinate] (14-16) at ($1*(x1)+4*(x2)+-1*(x3)+6*(x4)$) {};
\node[coordinate] (1207) at ($1*(x1)+2*(x2)+0*(x3)+7*(x4)$) {};
\node[coordinate] (3502) at ($3*(x1)+5*(x2)+0*(x3)+2*(x4)$) {};
\node[coordinate] (3421) at ($3*(x1)+4*(x2)+2*(x3)+1*(x4)$) {};
\node[coordinate] (1603) at ($1*(x1)+6*(x2)+0*(x3)+3*(x4)$) {};
\node[coordinate] (25-14) at ($2*(x1)+5*(x2)+-1*(x3)+4*(x4)$) {};
\node[coordinate] (34-25) at ($3*(x1)+4*(x2)+-2*(x3)+5*(x4)$) {};
\node[coordinate] (0712) at ($0*(x1)+7*(x2)+1*(x3)+2*(x4)$) {};
\node[coordinate] (-1542) at ($-1*(x1)+5*(x2)+4*(x3)+2*(x4)$) {};
\node[coordinate] (0631) at ($0*(x1)+6*(x2)+3*(x3)+1*(x4)$) {};
\node[coordinate] (2530) at ($2*(x1)+5*(x2)+3*(x3)+0*(x4)$) {};
\node[coordinate] (0271) at ($0*(x1)+2*(x2)+7*(x3)+1*(x4)$) {};
\node[coordinate] (-1461) at ($-1*(x1)+4*(x2)+6*(x3)+1*(x4)$) {};
\node[coordinate] (1360) at ($1*(x1)+3*(x2)+6*(x3)+0*(x4)$) {};
\node[coordinate] (245-1) at ($2*(x1)+4*(x2)+5*(x3)+-1*(x4)$) {};
\node[coordinate] (7012) at ($7*(x1)+0*(x2)+1*(x3)+2*(x4)$) {};
\node[coordinate] (6103) at ($6*(x1)+1*(x2)+0*(x3)+3*(x4)$) {};
\node[coordinate] (6-114) at ($6*(x1)+-1*(x2)+1*(x3)+4*(x4)$) {};
\node[coordinate] (5-234) at ($5*(x1)+-2*(x2)+3*(x3)+4*(x4)$) {};
\node[coordinate] (6031) at ($6*(x1)+0*(x2)+3*(x3)+1*(x4)$) {};
\node[coordinate] (5-142) at ($5*(x1)+-1*(x2)+4*(x3)+2*(x4)$) {};
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\node[coordinate] (52-14) at ($5*(x1)+2*(x2)+-1*(x3)+4*(x4)$) {};
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\node[coordinate] (43-25) at ($4*(x1)+3*(x2)+-2*(x3)+5*(x4)$) {};
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\node[coordinate] (5-106) at ($5*(x1)+-1*(x2)+0*(x3)+6*(x4)$) {};
\node[coordinate] (0-165) at ($0*(x1)+-1*(x2)+6*(x3)+5*(x4)$) {};
\node[coordinate] (4-253) at ($4*(x1)+-2*(x2)+5*(x3)+3*(x4)$) {};
\node[coordinate] (4-161) at ($4*(x1)+-1*(x2)+6*(x3)+1*(x4)$) {};
\node[coordinate] (2071) at ($2*(x1)+0*(x2)+7*(x3)+1*(x4)$) {};
\node[coordinate] (3160) at ($3*(x1)+1*(x2)+6*(x3)+0*(x4)$) {};
\node[coordinate] (425-1) at ($4*(x1)+2*(x2)+5*(x3)+-1*(x4)$) {};
\node[coordinate] (-2543) at ($-2*(x1)+5*(x2)+4*(x3)+3*(x4)$) {};
\node[coordinate] (-1605) at ($-1*(x1)+6*(x2)+0*(x3)+5*(x4)$) {};
\node[coordinate] (05-16) at ($0*(x1)+5*(x2)+-1*(x3)+6*(x4)$) {};
\node[coordinate] (45-12) at ($4*(x1)+5*(x2)+-1*(x3)+2*(x4)$) {};
\node[coordinate] (3601) at ($3*(x1)+6*(x2)+0*(x3)+1*(x4)$) {};
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\node[coordinate] (16-14) at ($1*(x1)+6*(x2)+-1*(x3)+4*(x4)$) {};
\node[coordinate] (35-24) at ($3*(x1)+5*(x2)+-2*(x3)+4*(x4)$) {};
\node[coordinate] (0721) at ($0*(x1)+7*(x2)+2*(x3)+1*(x4)$) {};
\node[coordinate] (-1641) at ($-1*(x1)+6*(x2)+4*(x3)+1*(x4)$) {};
\node[coordinate] (1630) at ($1*(x1)+6*(x2)+3*(x3)+0*(x4)$) {};
\node[coordinate] (254-1) at ($2*(x1)+5*(x2)+4*(x3)+-1*(x4)$) {};
\node[coordinate] (1270) at ($1*(x1)+2*(x2)+7*(x3)+0*(x4)$) {};
\node[coordinate] (-1560) at ($-1*(x1)+5*(x2)+6*(x3)+0*(x4)$) {};
\node[coordinate] (146-1) at ($1*(x1)+4*(x2)+6*(x3)+-1*(x4)$) {};
\node[coordinate] (345-2) at ($3*(x1)+4*(x2)+5*(x3)+-2*(x4)$) {};
\node[coordinate] (7102) at ($7*(x1)+1*(x2)+0*(x3)+2*(x4)$) {};
\node[coordinate] (7021) at ($7*(x1)+0*(x2)+2*(x3)+1*(x4)$) {};
\node[coordinate] (61-14) at ($6*(x1)+1*(x2)+-1*(x3)+4*(x4)$) {};
\node[coordinate] (6-105) at ($6*(x1)+-1*(x2)+0*(x3)+5*(x4)$) {};
\node[coordinate] (5-243) at ($5*(x1)+-2*(x2)+4*(x3)+3*(x4)$) {};
\node[coordinate] (6-141) at ($6*(x1)+-1*(x2)+4*(x3)+1*(x4)$) {};
\node[coordinate] (6130) at ($6*(x1)+1*(x2)+3*(x3)+0*(x4)$) {};
\node[coordinate] (6301) at ($6*(x1)+3*(x2)+0*(x3)+1*(x4)$) {};
\node[coordinate] (54-12) at ($5*(x1)+4*(x2)+-1*(x3)+2*(x4)$) {};
\node[coordinate] (53-24) at ($5*(x1)+3*(x2)+-2*(x3)+4*(x4)$) {};
\node[coordinate] (5320) at ($5*(x1)+3*(x2)+2*(x3)+0*(x4)$) {};
\node[coordinate] (524-1) at ($5*(x1)+2*(x2)+4*(x3)+-1*(x4)$) {};
\node[coordinate] (50-16) at ($5*(x1)+0*(x2)+-1*(x3)+6*(x4)$) {};
\node[coordinate] (5-160) at ($5*(x1)+-1*(x2)+6*(x3)+0*(x4)$) {};
\node[coordinate] (2170) at ($2*(x1)+1*(x2)+7*(x3)+0*(x4)$) {};
\node[coordinate] (416-1) at ($4*(x1)+1*(x2)+6*(x3)+-1*(x4)$) {};
\node[coordinate] (435-2) at ($4*(x1)+3*(x2)+5*(x3)+-2*(x4)$) {};
\node[coordinate] (06-15) at ($0*(x1)+6*(x2)+-1*(x3)+5*(x4)$) {};
\node[coordinate] (46-11) at ($4*(x1)+6*(x2)+-1*(x3)+1*(x4)$) {};
\node[coordinate] (45-23) at ($4*(x1)+5*(x2)+-2*(x3)+3*(x4)$) {};
\node[coordinate] (2701) at ($2*(x1)+7*(x2)+0*(x3)+1*(x4)$) {};
\node[coordinate] (3610) at ($3*(x1)+6*(x2)+1*(x3)+0*(x4)$) {};
\node[coordinate] (452-1) at ($4*(x1)+5*(x2)+2*(x3)+-1*(x4)$) {};
\node[coordinate] (1720) at ($1*(x1)+7*(x2)+2*(x3)+0*(x4)$) {};
\node[coordinate] (-1650) at ($-1*(x1)+6*(x2)+5*(x3)+0*(x4)$) {};
\node[coordinate] (164-1) at ($1*(x1)+6*(x2)+4*(x3)+-1*(x4)$) {};
\node[coordinate] (354-2) at ($3*(x1)+5*(x2)+4*(x3)+-2*(x4)$) {};
\node[coordinate] (056-1) at ($0*(x1)+5*(x2)+6*(x3)+-1*(x4)$) {};
\node[coordinate] (7201) at ($7*(x1)+2*(x2)+0*(x3)+1*(x4)$) {};
\node[coordinate] (7120) at ($7*(x1)+1*(x2)+2*(x3)+0*(x4)$) {};
\node[coordinate] (60-15) at ($6*(x1)+0*(x2)+-1*(x3)+5*(x4)$) {};
\node[coordinate] (6-150) at ($6*(x1)+-1*(x2)+5*(x3)+0*(x4)$) {};
\node[coordinate] (614-1) at ($6*(x1)+1*(x2)+4*(x3)+-1*(x4)$) {};
\node[coordinate] (64-11) at ($6*(x1)+4*(x2)+-1*(x3)+1*(x4)$) {};
\node[coordinate] (6310) at ($6*(x1)+3*(x2)+1*(x3)+0*(x4)$) {};
\node[coordinate] (54-23) at ($5*(x1)+4*(x2)+-2*(x3)+3*(x4)$) {};
\node[coordinate] (542-1) at ($5*(x1)+4*(x2)+2*(x3)+-1*(x4)$) {};
\node[coordinate] (534-2) at ($5*(x1)+3*(x2)+4*(x3)+-2*(x4)$) {};
\node[coordinate] (506-1) at ($5*(x1)+0*(x2)+6*(x3)+-1*(x4)$) {};
\node[coordinate] (56-10) at ($5*(x1)+6*(x2)+-1*(x3)+0*(x4)$) {};
\node[coordinate] (2710) at ($2*(x1)+7*(x2)+1*(x3)+0*(x4)$) {};
\node[coordinate] (461-1) at ($4*(x1)+6*(x2)+1*(x3)+-1*(x4)$) {};
\node[coordinate] (453-2) at ($4*(x1)+5*(x2)+3*(x3)+-2*(x4)$) {};
\node[coordinate] (065-1) at ($0*(x1)+6*(x2)+5*(x3)+-1*(x4)$) {};
\node[coordinate] (7210) at ($7*(x1)+2*(x2)+1*(x3)+0*(x4)$) {};
\node[coordinate] (605-1) at ($6*(x1)+0*(x2)+5*(x3)+-1*(x4)$) {};
\node[coordinate] (65-10) at ($6*(x1)+5*(x2)+-1*(x3)+0*(x4)$) {};
\node[coordinate] (641-1) at ($6*(x1)+4*(x2)+1*(x3)+-1*(x4)$) {};
\node[coordinate] (543-2) at ($5*(x1)+4*(x2)+3*(x3)+-2*(x4)$) {};
\node[coordinate] (560-1) at ($5*(x1)+6*(x2)+0*(x3)+-1*(x4)$) {};
\node[coordinate] (650-1) at ($6*(x1)+5*(x2)+0*(x3)+-1*(x4)$) {};

\def\pointclouds{ (2-145) / (2-154) / (3-254) / (3-245) / (2035) / (3025) / (4-125) / (4-235) / (2134) / (3124) / (4123) / (5023) / (5-124) / (2143) / (3142) / (4132) / (2053) / (3052) , (3016) / (3025) / (4-125) / (4-116) / (3106) / (41-16) / (50-16) / (5-106) / (3205) / (42-15) / (52-14) / (61-14) / (60-15) / (3214) / (4213) / (5203) / (3124) / (4123) , (0163) / (0172) / (1072) / (1063) / (0253) / (1243) / (2143) / (2053) / (0352) / (1342) / (2341) / (3241) / (3142) / (0361) / (1360) / (2350) / (0271) / (1270) , (3412) / (3421) / (4321) / (4312) / (3502) / (45-12) / (54-12) / (5302) / (3601) / (46-11) / (56-10) / (65-10) / (64-11) / (3610) / (461-1) / (560-1) / (3520) / (452-1) , (-1056) / (-1065) / (0-165) / (0-156) / (-1146) / (0136) / (1036) / (1-146) / (-1245) / (0235) / (1234) / (2134) / (2035) / (-1254) / (0253) / (1243) / (-1164) / (0163) , (2305) / (2314) / (3214) / (3205) / (24-15) / (34-25) / (43-25) / (42-15) / (25-14) / (35-24) / (45-23) / (54-23) / (53-24) / (2503) / (3502) / (45-12) / (2413) / (3412) , (0127) / (0136) / (1036) / (1027) / (0217) / (1207) / (2107) / (2017) / (0316) / (1306) / (2305) / (3205) / (3106) / (0325) / (1324) / (2314) / (0235) / (1234) , (-1452) / (-1461) / (0361) / (0352) / (-1542) / (0532) / (1432) / (1342) / (-1641) / (0631) / (1630) / (2530) / (2431) / (-1650) / (065-1) / (164-1) / (-1560) / (056-1) , (0523) / (0532) / (1432) / (1423) / (0613) / (1603) / (2503) / (2413) / (0712) / (1702) / (2701) / (3601) / (3502) / (0721) / (1720) / (2710) / (0631) / (1630) , (-2345) / (-2354) / (-1254) / (-1245) / (-2435) / (-1425) / (0325) / (0235) / (-2534) / (-1524) / (0523) / (1423) / (1324) / (-2543) / (-1542) / (0532) / (-2453) / (-1452) , (-1416) / (-1425) / (0325) / (0316) / (-1506) / (05-16) / (14-16) / (1306) / (-1605) / (06-15) / (16-14) / (25-14) / (24-15) / (-1614) / (0613) / (1603) / (-1524) / (0523) }



    
    \foreach \a/\b/\c/\d/\e/\f/\g/\h/\i/\j/\k/\l/\m/\n/\o/\p/\q/\r in \pointclouds{
        \draw[fill=purple!50!black] \a -- \b -- \c -- \d -- \a;
        \draw[fill=purple!90!black] \a -- \e -- \f -- \g -- \h -- \d -- \a;
        \draw[fill=purple] \f -- \e -- \i -- \j -- \f;
        \draw[fill=purple] \g -- \f -- \j -- \k -- \l -- \m -- \g;
        \draw[fill=purple] \k -- \j -- \i -- \n -- \o -- \p -- \k;
        \draw[fill=purple!95!black] \q -- \n -- \i -- \e -- \a -- \b -- \q;
        \draw[fill=purple!60!black] \q -- \n -- \o  -- \r -- \q;
    }

\end{tikzpicture}
&
\begin{tikzpicture}[scale=0.2]
    %tikz doesn't support 4d coordinate systems. So I pieced it together with this
    \node[coordinate] (p1) at (1,0){};
    \node[coordinate] (p2) at (0,1){};
    \node[coordinate] (p3) at (-0.4,-0.2){};
    \node[coordinate] (x1) at ($(p1)+(p2)+(p3)$){};
    \node[coordinate] (x2) at ($(p1)-(p2)-(p3)$){};
    \node[coordinate] (x3) at ($(p3)-(p1)-(p2)$){};
    \node[coordinate] (x4) at ($(p2)-(p1)-(p3)$){};
    
\node[coordinate] (w1) at ($1*(x1)+-3*(x2)+1*(x3)+1*(x4)$) {};
\node[coordinate] (w2) at ($1*(x1)+1*(x2)+-3*(x3)+1*(x4)$) {};
\node[coordinate] (w3) at ($1*(x1)+1*(x2)+1*(x3)+-3*(x4)$) {};
\node[coordinate] (w4) at ($-3*(x1)+1*(x2)+1*(x3)+1*(x4)$) {};

\node[coordinate] (p1) at ($2/4*(w1)+-1/4*(w2)+0/4*(w3)+0/4*(w4)$) {};
\node[coordinate] (p2) at ($0/4*(w1)+2/4*(w2)+-1/4*(w3)+0/4*(w4)$) {};
\node[coordinate] (p3) at ($0/4*(w1)+0/4*(w2)+2/4*(w3)+-1/4*(w4)$) {};
\node[coordinate] (p4) at ($-1/4*(w1)+0/4*(w2)+0/4*(w3)+2/4*(w4)$) {};

\node[coordinate] (1423) at ($1*(p1)+4*(p2)+2*(p3)+3*(p4)$) {};
\node[coordinate] (1432) at ($1*(p1)+4*(p2)+3*(p3)+2*(p4)$) {};
\node[coordinate] (4123) at ($4*(p1)+1*(p2)+2*(p3)+3*(p4)$) {};
\node[coordinate] (4132) at ($4*(p1)+1*(p2)+3*(p3)+2*(p4)$) {};
\node[coordinate] (1243) at ($1*(p1)+2*(p2)+4*(p3)+3*(p4)$) {};
\node[coordinate] (1234) at ($1*(p1)+2*(p2)+3*(p3)+4*(p4)$) {};
\node[coordinate] (2143) at ($2*(p1)+1*(p2)+4*(p3)+3*(p4)$) {};
\node[coordinate] (2134) at ($2*(p1)+1*(p2)+3*(p3)+4*(p4)$) {};
\node[coordinate] (3421) at ($3*(p1)+4*(p2)+2*(p3)+1*(p4)$) {};
\node[coordinate] (3412) at ($3*(p1)+4*(p2)+1*(p3)+2*(p4)$) {};
\node[coordinate] (4321) at ($4*(p1)+3*(p2)+2*(p3)+1*(p4)$) {};
\node[coordinate] (4312) at ($4*(p1)+3*(p2)+1*(p3)+2*(p4)$) {};
\node[coordinate] (3241) at ($3*(p1)+2*(p2)+4*(p3)+1*(p4)$) {};
\node[coordinate] (3214) at ($3*(p1)+2*(p2)+1*(p3)+4*(p4)$) {};
\node[coordinate] (2341) at ($2*(p1)+3*(p2)+4*(p3)+1*(p4)$) {};
\node[coordinate] (2314) at ($2*(p1)+3*(p2)+1*(p3)+4*(p4)$) {};
\node[coordinate] (1324) at ($1*(p1)+3*(p2)+2*(p3)+4*(p4)$) {};
\node[coordinate] (1342) at ($1*(p1)+3*(p2)+4*(p3)+2*(p4)$) {};
\node[coordinate] (3124) at ($3*(p1)+1*(p2)+2*(p3)+4*(p4)$) {};
\node[coordinate] (3142) at ($3*(p1)+1*(p2)+4*(p3)+2*(p4)$) {};
\node[coordinate] (2431) at ($2*(p1)+4*(p2)+3*(p3)+1*(p4)$) {};
\node[coordinate] (2413) at ($2*(p1)+4*(p2)+1*(p3)+3*(p4)$) {};
\node[coordinate] (4231) at ($4*(p1)+2*(p2)+3*(p3)+1*(p4)$) {};
\node[coordinate] (4213) at ($4*(p1)+2*(p2)+1*(p3)+3*(p4)$) {};

%\node at (p1) {p1};
%\node at (p2) {p2};
%\node at (p3) {p3};
%\node at (p4) {p4};
%\node at (w1) {w1};
%\node at (w2) {w2};
%\node at (w3) {w3};
%\node at (w4) {w4};
%\node at (0,0) {0};
%the edges are a mess, sorry

    \draw[dotted] (2143) -- (2134);
    \draw[dotted] (2143) -- (1243); 
    \draw[dotted] (4321) -- (4312); 
    \draw[dotted] (3421) -- (4321);
    \draw[dotted] (2341) -- (2431);
    \draw[dotted] (2341) -- (1342); 
    \draw[dotted] (3241) -- (2341);
    \draw[dotted] (3142) -- (3241);
    \draw[dotted] (4231) -- (3241);
    \draw[dotted] (4132) -- (4231); 
    \draw[dotted] (4321) -- (4231);
    \draw[dotted] (2143) -- (3142);
    \draw[dotted] (3142) -- (4132);
    \draw[dotted] (4132) -- (4123);
    
    \draw (4123) -- (4213);
    \draw (2134) -- (1234); 
    \draw (2431) -- (1432); 
    \draw (3421) -- (3412);
    \draw (3124) -- (3214); 
    \draw (2314) -- (1324); 
    \draw (2413) -- (1423);
    \draw (2431) -- (3421);
    \draw (4123) -- (3124);
    \draw (3124) -- (2134);
    \draw (1234) -- (1243);
    \draw (1243) -- (1342);
    \draw (1342) -- (1432);
    \draw (1432) -- (1423);
    \draw (1423) -- (1324);
    \draw (1324) -- (1234);
    \draw (4312) -- (4213);
    \draw (4213) -- (3214);
    \draw (3214) -- (2314);
    \draw (2314) -- (2413);
    \draw (2413) -- (3412);
    \draw (3412) -- (4312);
\end{tikzpicture}




    \end{tabular}