t = {{0.00000, 0.00000, 0.00000, 
            0.54983}, {1.13993, 1.13993, 1.13993, 1.42459}, {2.10579, 
            2.10579, 2.10579, 0.24832}, {2.93073, 2.93073, 1.34023, 
            1.14709}, {1.34023, 2.93073, 2.93073, 1.14709}, {2.93073, 
            1.34023, 2.93073, 1.14709}, {-1.13993, -1.13993, 1.13993, 
            1.42459}, {-2.10579, -2.10579, 2.10579, 
            0.24832}, {-2.93073, -2.93073, 1.34023, 
            1.14709}, {-1.34023, -2.93073, 2.93073, 
            1.14709}, {-2.93073, -1.34023, 2.93073, 
            1.14709}, {1.13993, -1.13993, -1.13993, 
            1.42459}, {2.10579, -2.10579, -2.10579, 
            0.24832}, {2.93073, -1.34023, -2.93073, 
            1.14709}, {2.93073, -2.93073, -1.34023, 
            1.14709}, {1.34023, -2.93073, -2.93073, 
            1.14709}, {-1.13993, 1.13993, -1.13993, 
            1.42459}, {-2.10579, 2.10579, -2.10579, 
            0.24832}, {-1.34023, 2.93073, -2.93073, 
            1.14709}, {-2.93073, 1.34023, -2.93073, 
            1.14709}, {-2.93073, 2.93073, -1.34023, 
            1.14709}};
u = {{0.00000, 0.00000, 0.00000}, {2.10579, 2.10579, 
            2.10579}, {3.30003, 3.30003, 0.99752}, {0.99752, 3.30003, 
            3.30003}, {3.30003, 0.99752, 
            3.30003}, {-2.10579, -2.10579, 
            2.10579}, {-3.30003, -3.30003, 
            0.99752}, {-0.99752, -3.30003, 
            3.30003}, {-3.30003, -0.99752, 
            3.30003}, {2.10579, -2.10579, -2.10579}, {3.30003, -0.99752, -3.30003}, {3.30003, -3.30003, -0.99752}, {0.99752, -3.30003, -3.30003}, {-2.10579, 
            2.10579, -2.10579}, 
{-0.99752, 
            3.30003, -3.30003}, 
{-3.30003, 
            0.99752, -3.30003}, 
{-3.30003, 
            3.30003, -0.99752}};

x = Table[t[[i, 1]], {i, 1, 21}];
y = Table[t[[i, 2]], {i, 1, 21}];
z = Table[t[[i, 3]], {i, 1, 21}];
r = Table[t[[i, 4]], {i, 1, 21}];
sq = Sqrt[2]/2;
h = Table[u[[i, 1]], {i, 1, 17}];
k = Table[u[[i, 2]], {i, 1, 17}];
l = 
        Table[u[[i, 3]], {i, 1, 17}];

(* 
      xy plane *) 
plot2=Graphics[{Circle[{x[[1]], y[[1]]}, 
            r[[1]]], 
Circle[{x[[2]], y[[2]]}, 
            r[[2]]], Circle[{x[[9]], y[[9]]}, r[[9]]], 
          Circle[{x[[3]], y[[3]]}, r[[3]]], 
          Circle[{x[[10]], y[[10]]}, r[[10]]], 
          Circle[{x[[4]], y[[4]]}, r[[4]]], 
          Circle[{x[[11]], y[[11]]}, r[[11]]], 
          Circle[{x[[5]], y[[5]]}, r[[5]]], 
          Circle[{x[[12]], y[[12]]}, r[[12]]], 
          Circle[{x[[6]], y[[6]]}, r[[6]]], 
          Circle[{x[[13]], y[[13]]}, r[[13]]], 
          Circle[{x[[7]], y[[7]]}, r[[7]]], 
          Circle[{x[[14]], y[[14]]}, r[[14]]], 
          Circle[{x[[8]], y[[8]]}, r[[8]]], 
          Circle[{x[[15]], y[[15]]}, r[[15]]], 
          Circle[{x[[16]], y[[16]]}, r[[16]]], 
          Circle[{x[[17]], y[[17]]}, r[[17]]], 
          Circle[{x[[18]], y[[18]]}, r[[18]]], 
          Circle[{x[[19]], y[[19]]}, r[[19]]], 
          Circle[{x[[20]], y[[20]]}, r[[20]]], 
          Circle[{x[[21]], y[[21]]}, r[[21]]], 
          Disk[{h[[1]], k[[1]]}, 0.08],  
          Disk[{h[[2]], k[[2]]}, 0.08],  
          Disk[{h[[3]], k[[3]]}, 0.08],  
          Disk[{h[[4]], k[[4]]}, 0.08],  
          Disk[{h[[5]], k[[5]]}, 0.08], 
          Disk[{h[[6]], k[[6]]}, 0.08],  
          Disk[{h[[7]], k[[7]]}, 0.08],  
          Disk[{h[[8]], k[[8]]}, 0.08],  
          Disk[{h[[9]], k[[9]]}, 0.08],  
          Disk[{h[[10]], k[[10]]}, 0.08], 
          Disk[{h[[11]], k[[11]]}, 0.08],  
          Disk[{h[[12]], k[[12]]}, 0.08],  
          Disk[{h[[13]], k[[13]]}, 0.08],  
          Disk[{h[[14]], k[[14]]}, 0.08],  
          Disk[{h[[15]], k[[15]]}, 0.08], 
          Disk[{h[[16]], k[[16]]}, 0.08],  
          Disk[{h[[17]], k[[17]]}, 0.08], Thickness[0.006], 
          Line[{{h[[2]], k[[2]]}, {h[[3]], k[[3]]}}], 
          Line[{{h[[4]], k[[4]]}, {h[[5]], 
                k[[5]]}}] } ]

Show[
      plot2, {AspectRatio  ->  Automatic, Axes  ->  True, 
        GridLines  ->  Automatic,  
        PlotRange  ->  {{-4.75, 4.75}, {-4.75, 4.75}},  
        Frame  ->  True}]

  
plot3 = 
      Graphics[{Circle[{x[[1]], z[[1]]}, 
            r[[1]]], 
Circle[{sq*x[[2]] - 
                sq*y[[2]], z[[2]]}, r[[2]]], 
          Circle[{sq*x[[3]] - sq*y[[3]], z[[3]]}, r[[3]]], 
          Circle[{sq*x[[4]] - sq*y[[4]], z[[4]]}, r[[4]]], 
          Circle[{sq*x[[5]] - sq*y[[5]], z[[5]]}, r[[5]]], 
          Circle[{sq*x[[6]] - sq*y[[6]], z[[6]]}, r[[6]]], 
          Circle[{sq*x[[7]] - sq*y[[7]], z[[7]]}, r[[7]]], 
          Circle[{sq*x[[8]] - sq*y[[8]], z[[8]]}, r[[8]]], 
          Circle[{sq*x[[9]] - sq*y[[9]], z[[9]]}, r[[9]]], 
          Circle[{sq*x[[10]] - sq*y[[10]], z[[10]]}, 
            r[[10]]], 
          Circle[{sq*x[[11]] - sq*y[[11]], z[[11]]}, 
            r[[11]]], 
          Circle[{sq*x[[12]] - sq*y[[12]], z[[12]]}, 
            r[[12]]], 
          Circle[{sq*x[[13]] - sq*y[[13]], z[[13]]}, 
            r[[13]]], 
          Circle[{sq*x[[14]] - sq*y[[14]], z[[14]]}, 
            r[[14]]], 
          Circle[{sq*x[[15]] - sq*y[[15]], z[[15]]}, 
            r[[15]]], 
          Circle[{sq*x[[16]] - sq*y[[16]], z[[16]]}, 
            r[[16]]], 
          Circle[{sq*x[[17]] - sq*y[[17]], z[[17]]}, 
            r[[17]]], 
          Circle[{sq*x[[18]] - sq*y[[18]], z[[18]]}, 
            r[[18]]], 
          Circle[{sq*x[[19]] - sq*y[[19]], z[[19]]}, 
            r[[19]]], 
          Circle[{sq*x[[20]] - sq*y[[20]], z[[20]]}, 
            r[[20]]], 
          Circle[{sq*x[[21]] - sq*y[[21]], z[[21]]}, 
            r[[21]]], 
          Disk[{sq*x[[3]] - sq*y[[3]], z[[3]]}, 0.08],  
          Disk[{sq*x[[8]] - sq*y[[8]], z[[8]]}, 0.08],  
          Disk[{sq*x[[13]] - sq*y[[13]], z[[13]]}, 0.08],  
          Disk[{sq*x[[18]] - sq*y[[18]], z[[18]]}, 0.08],  
          Disk[{0, 0}, 0.08],  
          Disk[{sq*(h[[3]] - k[[3]]), l[[3]]}, 0.08],  
          Disk[{sq*(h[[4]] - k[[4]]), l[[4]]}, 0.08],  
          Disk[{sq*(h[[5]] - k[[5]]), l[[5]]}, 0.08], 
          Disk[{sq*(h[[7]] - k[[7]]), l[[7]]}, 0.08],  
          Disk[{sq*(h[[8]] - k[[8]]), l[[8]]}, 0.08],  
          Disk[{sq*(h[[9]] - k[[9]]), l[[9]]}, 0.08], 
          Disk[{sq*(h[[11]] - k[[11]]), l[[11]]}, 0.08],  
          Disk[{sq*(h[[12]] - k[[12]]), l[[12]]}, 0.08],  
          Disk[{sq*(h[[13]] - k[[13]]), l[[13]]}, 0.08],  
          Disk[{sq*(h[[15]] - k[[15]]), l[[15]]}, 0.08], 
          Disk[{sq*(h[[16]] - k[[16]]), l[[16]]}, 0.08],  
          Disk[{sq*(h[[17]] - k[[17]]), l[[17]]}, 
            0.08], {Thickness[0.006], 
            Line[{{sq*x[[8]] - sq*y[[8]], z[[8]]}, {0, 0}}], 
            Line[{{sq*x[[13]] - sq*y[[13]], z[[13]]}, {0, 0}}], 
            Line[{{sq*x[[18]] - sq*y[[18]], z[[18]]}, {0, 0}}], 
            Line[{{sq*x[[3]] - sq*y[[3]], z[[3]]}, {0, 
                  0}}]}}]
Show[
      plot3, {AspectRatio  ->  Automatic, Axes  ->  True, 
        GridLines  ->  Automatic,  
        PlotRange  ->  {{-6, 6}, {-5, 5}},  
        Frame  ->  True}]

w = Sqrt[2/3];  
    v = Sqrt[1/3];    

plot4 = 
      Graphics[{Circle[{x[[1]], z[[1]]}, 
            r[[1]]], 
Circle[{w*(sq*x[[2]] - 
                    sq*y[[2]]), w*z[[2]]}, r[[2]]], 
          Circle[{sq*x[[3]] - sq*y[[3]], w*z[[3]]}, r[[3]]], 
          Circle[{sq*x[[4]] - sq*y[[4]], w*z[[4]]}, r[[4]]], 
          Circle[{sq*x[[5]] - sq*y[[5]], w*z[[5]]}, r[[5]]], 
          Circle[{sq*x[[6]] - sq*y[[6]], w*z[[6]]}, r[[6]]], 
          Circle[{sq*x[[7]] - sq*y[[7]], w*z[[7]]}, r[[7]]], 
          Circle[{sq*x[[8]] - sq*y[[8]], w*z[[8]]}, r[[8]]], 
          Circle[{sq*x[[9]] - sq*y[[9]], w*z[[9]]}, r[[9]]], 
          Circle[{sq*x[[10]] - sq*y[[10]], w*z[[10]]}, 
            r[[10]]], 
          Circle[{sq*x[[11]] - sq*y[[11]], w*z[[11]]}, 
            r[[11]]], 
          Circle[{sq*x[[12]] - sq*y[[12]], w*z[[12]]}, 
            r[[12]]], 
          Circle[{sq*x[[13]] - sq*y[[13]], w*z[[13]]}, 
            r[[13]]], 
          Circle[{sq*x[[14]] - sq*y[[14]], w*z[[14]]}, 
            r[[14]]], 
          Circle[{sq*x[[15]] - sq*y[[15]], w*z[[15]]}, 
            r[[15]]], 
          Circle[{sq*x[[16]] - sq*y[[16]], w*z[[16]]}, 
            r[[16]]], 
          Circle[{sq*x[[17]] - sq*y[[17]], w*z[[17]]}, 
            r[[17]]], 
          Circle[{sq*x[[18]] - sq*y[[18]], w*z[[18]]}, 
            r[[18]]], 
          Circle[{sq*x[[19]] - sq*y[[19]], w*z[[19]]}, 
            r[[19]]], 
          Circle[{sq*x[[20]] - sq*y[[20]], w*z[[20]]}, 
            r[[20]]], 
          Circle[{sq*x[[21]] - sq*y[[21]], w*z[[21]]}, 
            r[[21]]], 
          Disk[{sq*x[[3]] - sq*y[[3]], w*z[[3]]}, 0.08],  
          Disk[{sq*x[[8]] - sq*y[[8]], w*z[[8]]}, 0.08],  
          Disk[{sq*x[[13]] - sq*y[[13]], w*z[[13]]}, 0.08],  
          Disk[{sq*x[[18]] - sq*y[[18]], w*z[[18]]}, 0.08],  
          Disk[{0, 0}, 0.08], {Thickness[0.006], 
            Line[{{sq*x[[8]] - sq*y[[8]], w*z[[8]]}, {0, 0}}], 
            Line[{{sq*x[[13]] - sq*y[[13]], w*z[[13]]}, {0, 0}}], 
            Line[{{sq*x[[18]] - sq*y[[18]], w*z[[18]]}, {0, 0}}], 
            Line[{{sq*x[[3]] - sq*y[[3]], w*z[[3]]}, {0, 
                  0}}]}}]
Show[
      plot4, {AspectRatio  ->  Automatic, Axes  ->  True, 
        GridLines  ->  Automatic,  
        PlotRange  ->  {{-6, 6}, {-6, 6}},  
        Frame  ->  True}]