Cubic Seki

    Keywords: Theory

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 ?

[Diagram]

  • 8 x 10 intersections
  • 34 stones each
  • 3 liberties each
  • no square (2x2 block)



Here's one not depending on edges:

[Diagram]

  • 8 x 12 intersections
  • 42 stones each
  • 3 liberties each
  • no square
  • no edge




Nicest ?

[Diagram]

  • 10 x 10 intersections
  • 44 stones each
  • 3 liberties each
  • no square



Or rather this one?

[Diagram]

  • 10 x 10 intersections
  • 44 stones each
  • 3 liberties each
  • no square




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:

[Diagram]

i = 0



[Diagram]

i = 1



[Diagram]

i = 2



etc., giving

  • (12 + 2i) x (12 + 2i) intersections
  • 66 + 18i + 2ii stones each
  • 3 + 3i liberties each

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


This is a copy of the living page "Cubic Seki" at Sensei's Library.
(OC) 2009 the Authors, published under the OpenContent License V1.0.
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