The shuffle kitten

Since Steiner systems $S(5,6,12)$ are unique up to relabelings, we should expect a ``kitten'' for the shuffle labeling. There is one and this section describes it. In Conway, [Co1], the MINIMOG for the ``modulo 11 labeling'' is given:

$$\begin{array}{cccc} 0 & 3 & \infty & 2\\ 5 & 9 & 8 & 10 \\ 4 & 1 & 6 & 7 \end{array}$$

Comparing this MINIMOG with that for the shuffle labeling, we obtain the following kitten.

					6
					9
				10		8
			7		2		5
		9		4		11		9
	10		8		3		10		8
1										0

The Shuffle Kitten.

The ``views'' from each of the three ``points at infinity'' is given in the following tables.

5	11	3
8	2	4
9	10	7

5	11	3
2	4	8
7	9	10

8	10	3
9	11	4
5	2	7

picture at $6$

picture at $1$

picture at $0$

Example 5  

• 0,2,4,5,6,11 is a square in the picture at 1.
• 0,2,3,4,5,7 is a cross in the picture at 0.