The question is:

vertices = {{0, 0, Sqrt[2/3] - 1/(2 Sqrt[6])}, {0, 
    Sqrt[3]/3, -1/(2 Sqrt[6])}, {-1/2, -Sqrt[3]/
     6, -1/(2 Sqrt[6])}, {1/2, -Sqrt[3]/6, -1/(2 Sqrt[6])}   };


scale = (6 Sqrt[2])/Sqrt[Total[(vertices[[1]] - vertices[[2]])^2]];
scaledVertices = scale*vertices;


center = Mean[scaledVertices];


a = 6 Sqrt[2]; 
h = a Sqrt[2/3]; 
R = 3/4 h; 
r_inner = h/4; 
maxBlackRadius = R - 1; 


hydrogenBalls = Table[Sphere[scaledVertices[[i]], 1], {i, 4}];
carbonBall = Sphere[center, maxBlackRadius]; 
sticks = Table[Cylinder[{center, scaledVertices[[i]]}, 0.1], {i, 4}];

modelPlot = 
 Graphics3D[{{White, Opacity[0.8], hydrogenBalls}, {Black, 
    Opacity[0.8], carbonBall}, {Gray, Opacity[0.6], sticks}, {Red, 
    PointSize[0.02], Point[center]}, {Blue, PointSize[0.02], 
    Point[scaledVertices]}}, Boxed -> True, Lighting -> "Neutral", 
  ViewPoint -> {1, 1, 1}, ImageSize -> 500, PlotLabel -> "Model"]

My question is: According to the requirements of the problem, what are some good methods to draw the three-dimensional structure of methane, and to draw a circumscribed regular tetrahedron that can accommodate this structure while meeting the requirements, and to determine the correctness of the four options.