Lighting in the round is a whole different thing from lighting
proscenium and thrust-stage productions to be certain. I have done some designing for
Theatre in the Round Players in Minneapolis. That
arena has an irregular shape that can best be described as an irregular heptagon that is roughly 25 feet (7.5 M) across at any given
point.
Grid is at 14 feet.
For your space which is roughly 13 by 17 feetI would say that the minimum number of "areas" that you can get by with is 6. This should work if your cans can give a beam spread of about 40-45 degrees. If you did the most basic 3-point
system with lights placed at 180 degree angles to each other you would need a minimum of 18 lights.
If possible I recommend a 4-point
system with an additional toplight for each acting area for starters. I like to bring these in at a slightly higher angle than 45 degrees (usually 50 to 55 degrees) to help avoid
spill into the audience's eyes. Since the audience is usually very close I find that it works fine. It is best if this
system is done at a 45 degree angle (left and right) to a
line perpendicular to each of the 4 sides. In a 4-point
system I usually pair the lights that are 180 degrees apart with one pair being a pastel warm and the other being a pastel cool. Of course with
LED lights you have a lot of options to
play here over the course of a program. To this I would then add a top light for each area and use more saturated colors: lavenders, blues, magentas,
etc.. For a
system such as this you would need a minimum of 30 fixtures. This would be what you have called your "near shot" lights.
Once this is done I would create a secondary
system consisting of 6 to 8 lights that are at a much lower angle and further away from the
stage. I would bring these in "head-on" (perpendicular to the seating areas) at about a 35 degree angle. These lights, along with the top lights would be used primarily for saturated color washes and possibly bright white when desired for the
effect. This
system would be the closest thing to what you
call "far shot" lights.
Now, If you had any ellipsoidals or moving lights, you could created some
tertiary pattern washes at an intermediate angle of 40 degrees or so that would add even more interest and texture.