14.16.1  Cubes: cube

The cube command creates cubes.

• cube takes three arguments:
  A,B,C, three points.
• cube(A,B,C) returns and draws the following cube:
  • One edge is AB.
  • One face is in the plane ABC, on the same side of line AB as is C.
  • The cube is on the side of plane ABC that makes the points A, B and C counterclockwise.

Examples.

• Input:
  C1:= cube([0,0,0],[0,4,0],[0,0,1])
  Output:
  
  Input:
  c1,c2,c3,c4,c5,c6,c7,c8:= vertices(C1)
  Output:
  
  Input:
  faces(C1)
  Output:

  ⎡ ⎣

  ⎡ ⎣

  ⎡ ⎣

  0,0,0

  ⎤ ⎦

  ,

  ⎡ ⎣

  0,4,0

  ⎤ ⎦

  ,

  ⎡ ⎣

  0,4,4

  ⎤ ⎦

  ,

  ⎡ ⎣

  0,0,4

  ⎤ ⎦

  ⎤ ⎦

  ,

  ⎡ ⎣

  ⎡ ⎣

  4,0,0

  ⎤ ⎦

  ,

  ⎡ ⎣

  4,4,0

  ⎤ ⎦

  ,

  ⎡ ⎣

  4,4,4

  ⎤ ⎦

  ,

  ⎡ ⎣

  4,0,4

  ⎤ ⎦

  ⎤ ⎦

  ,

  ⎡ ⎣

  ⎡ ⎣

  0,0,0

  ⎤ ⎦

  ,

  ⎡ ⎣

  4,0,0

  ⎤ ⎦

  ,

  ⎡ ⎣

  4,0,4

  ⎤ ⎦

  ,

  ⎡ ⎣

  0,0,4

  ⎤ ⎦

  ⎤ ⎦

  ,

  ⎡ ⎣

  ⎡ ⎣

  0,0,0

  ⎤ ⎦

  ,

  ⎡ ⎣

  0,4,0

  ⎤ ⎦

  ,

  ⎡ ⎣

  4,4,0

  ⎤ ⎦

  ,

  ⎡ ⎣

  4,0,0

  ⎤ ⎦

  ⎤ ⎦

  ,

  ⎡ ⎣

  ⎡ ⎣

  0,4,0

  ⎤ ⎦

  ,

  ⎡ ⎣

  0,4,4

  ⎤ ⎦

  ,

  ⎡ ⎣

  4,4,4

  ⎤ ⎦

  ,

  ⎡ ⎣

  4,4,0

  ⎤ ⎦

  ⎤ ⎦

  ,

  ⎡ ⎣

  ⎡ ⎣

  0,0,4

  ⎤ ⎦

  ,

  ⎡ ⎣

  4,0,4

  ⎤ ⎦

  ,

  ⎡ ⎣

  4,4,4

  ⎤ ⎦

  ,

  ⎡ ⎣

  0,4,4

  ⎤ ⎦

  ⎤ ⎦

  ⎤ ⎦

• Input:
  C2:= cube([0,0,0],[0,4,0],[0,0,-1])
  Output:
  
  Input:
  a1,a2,a3,a4,a5,a6,a7,a8:= vertices(C2)
  Output: