@Kitonum Thank you very much. I don't know, by using your code for the S(0,0,sqrt(2)/2), the dihedral not equalt to 3*Pi/4. 

@mmcdara  Please note that "When the two intersecting planes", my quesiton is dihedral angle of two halfplanes. 

@Carl Love  Please note that "When the two intersecting planes", my quesiton is dihedral angle of two halfplanes. 

@Carl Love I want to calculate dihedral angle of two halfplanes not angle two planes, https://en.wikipedia.org/wiki/Dihedral_angle,  I think, the answers are 2*Pi/3 and 3*Pi/4. 

@Kitonum Thank you very much.

@sand15 I am sorry, I don't know how he did it. 

@sand15 My friend uses  asymptote https://asymptote.sourceforge.io/ and get the result

@mmcdara I don't say "with n = 14, The answer of Maple and your result are different." but I said There are differences between the two programs at the end of the questions when I compare two cases n = 14 and n = 15. 

@mmcdara with n = 14, The answer of Mathamatica and your result are different.

@nm How can I write solution to this mylist? 
We have, vector AB = (),  vector AC = ( ). Normal vector of the plane ABC is Crossproduct(AB, AC). The equation of equation ABC is 

@nm Thank you very much.

@vv Thank you very much. 

@Kitonum My code is slower than your. How can I reduce the time compile?

restart;
with(Student[MultivariateCalculus]);
A := [0, 0, 4];
B := [6, -2, 6];
M := [x, y, z];
d := Line(<1, -1, 2>, [4, -8, 4]);
f := Distance(M, d);
p := (Student[MultivariateCalculus]):-`.`(<x, y, z> - <0, 0, 4>, <x, y, z> - <6, -2, 6>);
extrema(f, {p = 0, x^2 + (y - 2)^2 + (z + 1)^2 = 29}, {x, y, z}, s);
s;

@acer Thank you very much

@acer I tried this code and get massage "Warning, solve may be ignoring assumptions on the input variables." 

with(Student:-MultivariateCalculus);
A := [0, 0, 0];
B := [1, 0, 0];
C := [1, 1, 0];
DD := [0, 2, 0];
assume(0 < h);
S := [0, 0, h];
d1 := Line(S, C);
d2 := Line(B, DD);
cos(Angle(d1, d2));
P := Plane(A, B, C);
temp := Angle(d1, P);
solve(temp = Pi/3);