Polygons

A quadrilateral assignment is a list of 4 variable names followed by the word parallelogram, rectangle or square and some optional parameters. If the first variable is already defined as a point, the quadrilateral is constructed from this point. If not, the point is set to origin. The optional parameter b is the polar angle of segment AB (default: 0°). Here are all the ways to define a quadrilateral when the second variable is not already defined as a point:

• A B C D parallelogram[(x, y, a [, b])]
  Defines a parallelogram with AB = x, AD = y and angle under BAD equals a (default: 5, 4 and 75°).
• A B C D parallelogram(u, v [, b])
  Defines a parallelogram with vector from A to B equals u and vector from A to D equals v.
• A B C D rectangle[(x, y [, b])]
  Defines a rectangle with AB = x and AD = y (default: 6 and 6 / `golden ratio').
• A B C D square[(x [, b])]
  Defines a square with AB = x (default: 4).

Here are all the ways to define a quadrilateral when the first and the second variables are already defined as points:

• A B C D parallelogram(x, a)
  Defines a parallelogram with AD = x and angle under BAD equals a.
• A B C D rectangle(x)
  Defines a rectangle with AD = x.
• A B C D square
  Defines a square.

When the three first variables are already defined as points, one may also use:

• A B C D parallelogram
  
• A B C D rectangle
  

A pentagon assignment is the following command:

• A B C D E pentagon(F, x, a)
  It defines a pentagon of center F, radius x and such as polar angle of segment FA equals a.

An hexagon assignment is the following command:

• A B C D E F hexagon(G, x, a)
  It defines an hexagon of center G, side length x and such as polar angle of segment GA equals a.