Rectangular six
A group with a big eye with the shape of a rectangular six, is alive except for rectangular six in the corner.
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Rectangular six without cutting points
Here, the eyespace is at the side, but in the center the implications are the same. The vital points are a and b and they are miai, as shown in the following diagrams.
If White tenukis, playing elsewhere, White is still alive but now lives in seki: Black can at most almost fill with a bent four. However, this seki is not valid for rectangular six in the corner.
Rectangular six with cutting points
There are two cutting points (induced by ) in the otherwise ordinary looking rectangular six. Notice that one of the two chains has no outside liberties at all.
The status of this group is actually unsettled. If Black plays first, White can be killed. The Chinese calls this 断头板六.
Black can kill by playing the placement at and then cutting at
. Owing to shortage of liberties, a White move at a would be self-atari, so White can no longer form two eyes.
On the other hand, if the rectangular six group has two cutting points as shown, then it is still alive. The comb formation is essentially a rectangular six with two cutting points of this form. Life and death can be so strange.
See also