Cubic Seki
The topology of a cubic seki resembles that of a cube. Pressed flat, that's
X -------- O | \ / | | O -- X | | | | | | X -- O | | / \ | O -------- X
Eight corners - the groups - connected by twelve edges - their shared liberties.
Harry Fearnley:You could also think of this arrangement as a regular Octahedron -- a solid with 8 triangular faces. These are arranged to look like 2 (square-based) pyramids, which are glued together at their bases. The Octahedron is the dual of the Cube: it has has 8 faces, and 6 vertices (corners), whereas the Cube has 8 vertices, and 6 faces. Both have 12 edges, which mean essentially the same things -- in the Cube model they represent the fact that 2 groups are connected, whereas in the Octahedron they represent (equivalently) the existence of a shared border. In some ways, this is more natural -- you can think of the 8 groups being the 8 faces, and then imagine these laid out on a sphere ...
Smallest ?
- 8 x 10 intersections
- 34 stones each
- 3 liberties each
- no square (2x2 block)
Here's one not depending on edges:
Nicest ?
Generator
To increase the number of shared liberties, take the one below (made of the one above) and duplicate its two rows and two columns framing its 2x2 center:
Terminality
Robert Pauli: I guess nobody can gain anything if he starts - under territory scoring, of course (and under area scoring the gain might be equal). At i = 0 and i = 1 it's even disadvantageous. From i = 2 on, without having a proof, I feel that if both go after the weakest opposing group without touching the second to last liberty between them, nobody will be captured. True?
Authors