14.13.13  Checking if an object in space is a rhombus: is_rhombus

See Section 13.16.9 for checking for rhombuses in two-dimensional geometry.

The is_rhombus command determines whether or not a geometric object is a rhombus.

• is_rhombus takes one argument:
  G, a geometric object or a sequence of four points assumed to be the vertices of a quadrilateral.
• is_square(G) returns 1 if G is a rhombus but not a square, returns 2 if G is a square and returns 0 otherwise.

Examples.

• Input:
  is_rhombus([2,0,0],[0,1,0],[-2,0,0],[0,-1,0])
  Output:

  1

• Input:

  R:= rhombus([0,0,0],[2,0,0],[[0,0,1],pi/4])

  is_rhombus(S)

  Output:

  1

• Input:
  is_rhombus([2,2,0],[-2,2,0],[-2,-1,0],[2,-1,0])
  Output:

  0