14.8.1  Squares in space: square

See Section 13.9.1 for squares in the plane.

The square command creates squares.

• square takes three mandatory arguments and two optional arguments:
  • A,B,P, three points.
  • Optionally, var1,var2, two variable names.
• square(A,B,P ⟨,var1,var2⟩) returns and draws the square with one side AB and the remaining sides in the same half-plane as P.
  If the arguments var1 and var2 are given, they will be assigned to the new vertices.

Examples.

• Input:

  A:= point(0,0,0);

  B:= point(3,3,3);

  P:= point(0,0,3);

  square(A,B,P)

  Output:
  
• Input:

  A:= point(0,0,0); B:= point(3,3,3); P:= point(0,0,3); square(A,B,P,C,D) coordinates(C), coordinates(D)

  Output:

  ⎡ ⎢ ⎢ ⎣

  −3  √ 2 +6 2

  ,

  −3  √ 2 +6 2

  ,3

  √

  2

  +3

  ⎤ ⎥ ⎥ ⎦

  ,

  ⎡ ⎢ ⎢ ⎣

  −

  3 2

  √

  2

  ,−

  3 2

  √

  2

  ,3

  √

  2

  ⎤ ⎥ ⎥ ⎦