Rectangles in space: rectangle

### 13.8.3 Rectangles in space: rectangle

See section 12.9.3 for rectangles in the plane.

The rectangle command returns and draws a rectangle. It takes as arguments one of the following:

- Three points, A, B and P.
  rectangle(A,B,P) returns and draws the rectangle ABCD. The first two points A and B are vertices of the rectangle, the third point P determines the plane and orientation of the rectangle. The orientation is so that angle BAP is positive. The length of side AD equals the length of AP.
  Input:
  A := point(0,0,0); B := point(3,3,3);
  P := point(0,0,3)
  then:
  rectangle(A,B,P)
  Output:
- Two points, A and B, and a list consisting of a point P and a real number k.
  rectangle(A,B,[P,k]) returns and draws the rectangle ABCD. The first two points A and B are vertices of the rectangle, the third point P determines the plane and orientation of the rectangle as above. The length of AD is |k| times the length of AB. Angle BAD has the same orientation as BAP if k is positive, angle BAD has opposite orientation as BAP if k is negative.
  Input:
  rectangle(A,B,[P,1/2])
  Output:

rectangle takes optional fourth and fifth arguments, which are variables assigned to vertices C and D.
Input:

rectangle(A,B,P,C,D)

then:

simplify(coordinates(C)), simplify(coordinates(D))

Output:

[-(sqrt(6))/2,-(sqrt(6))/2,sqrt(6)],
[(-(sqrt(6))+6)/2,(-(sqrt(6))+6)/2,sqrt(6)+3]