[r-t] Extents of doubles

[Philip Earis]

Many thanks, Richard.

> Crambo is one of only eleven doubles extents (up to
> rotation, reflection, etc.) with the following properties:
>
>  - the extent forms a perfect five part (i.e. it is a
>    principle);
>
>  - no more than four consecutive blows in any one place;
>    and
>
>  - uses only single changes.

Can you provide a list of these 11?  What about if you ignore the 
restirction of four consecutive blows?



>> There are other interesting methods on the same webpage, from the 
>> familiar
>> Orpheus, to Mermaid 
>> (1.3.1.3.1.5.1.3.1.3.1.125.3.5.3.5.3.1.3.5.3.5.3.145),
>> which has some beautiful symmetry.
>
> OK.  What am I missing?  Mermaid doesn't have any symmetry,
> does it?

Taken as a whole, no, but it braks down nicely.  Clealy if a plain course is 
going to generate the extent, half of each 24 row division must be in 
course, and half out of course.  I like the way Mermaid has the minimum 
number of single changes - this kind of splits into two different methods. 
Mermaid further splits into four quarters too - a "1.3.1.3.1.5" block and a 
"3.5.3.5.3.1" (reverse erin rotated) block.


>> Can anyone generate an exhaustive list of all 24 change-per-lead doubles
>> principles whose plain course generates the extent?
>
> It ought to be feasible.

I look forward to the results!