This board gives an overview of the basic killing shapes.
If the stones are captured, the circled stone indicates where to play next to prevent two eyes (vital point).
Here they are again as spaces of marked points:
If no is given the shape is already only one eye.
The points marked are the vital points.
And this is how they will appear in games with a full border of black or white stones. If the border isn't complete the group has even less chance of life.
These are of course the same patterns three times over. The standard way to look at the shapes might be like this:
Here it is completely clear what is meant: the vital point is at a and the black group lives or dies according to whether Black can play there first.
The shapes, however, must be visualised in one or other way, to get answers about life and death questions. That may be long before the completed formations are in place on the board
This shape, a Greek cross, is the key killing shape, from which the others may be derived. The killing point to prevent two eyes (when these stones have been captured), is the center point . If you take away any other stone or stones from this shape you get another killing shape with the same killing point. In addition, if you add one stone to one of those shapes at a point (a) that is next to two of the arms of the cross, you also get a killing shape with the same killing point. (Some of these shapes have no unique killing point because the opponent cannot make two eyes with one move.)
You can learn more about these killing shapes at their separate pages:
- (One stone and two stones do not have a separate page)
- Straight three
- Bent three
- Square four
- Pyramid Four
- Bulky five
- Crossed five
- Rabbitty six
In the corner other killing shapes exist. The presence of cutting points also induces other killing shapes.
One corollary of all this is that a group that forms a single eye outside the corner with no cutting points that has eight or more points is alive unless the opponent can form an eye inside, or a ko. Often this is erroneously stated as an eight point eye is alive.
As per request on CoffeeMachine, I'll add a bit of information here for ease of reading. All of the above mentioned killing shapes have a vital point that can be exploited to kill any chance of two eyes. I will display them here. Many of these play out to be smaller shapes (for example, Five in a Cross often becomes Straight three or Bent three)
Network of killing shapes:
O O O O O -- O O O -- O O O / / \ O \ / / \ \ / / \ \ / O / O O O O O O O --- O O --- O O --- O O --- O O O --- O O O O
 This is almost true of the rabbity six, but you can form a bent four by removing two stones.