It was the section from N51 00.000 W000 00.000 to N51 59.999 W000 59.999 that initially caught parmstro's interest and gave birth to the series. However, that is just a tiny section of the line that takes its name from the point where it intersects with the Meridian. From its (arbitrary) starting point on the Meridian the line extends in two directions. To the Northwest through N52 W001, N53 W002 and so on, eventually coming to the North Pole and to the Northeast through N52 E001, N53 E002 and so on, also eventually coming to the North Pole. I tend to think of this forming a heart shape, though this is not quite right as the lines tranverse the surface of a sphere. Maybe somewhere between a heart and diamond shape?
There are 180 lines that cross the Meridian - N00 to N89 and S00 to S89. N0 and S0 are a special case as all the numbers are the same and they intersect with each other at the point where the Meridian crosses the Equator.Consider next the line that starts at N00 W001. To the Northwest it goes through N01 W002, N02 W003 and so on, eventually coming to the North Pole. To the Southwest it goes through S01 W002, S02 W003 and so on, eventually coming to the South Pole. All the lines from W01 to W90 and E01 to E90 run from the North to the South Poles. Whether you want to count that as 180 lines or just 90 lines I will leave up to you.
Finally, consider the line that starts at N00 W091. This runs up to N89 W180 where it meets its counterpart that started at N00 E091. It also runs to S89 W180 and again meets its counterpart that started at N00 E091. This holds true for the lines starting at N00 W091 to N00 W179 and N00 E091 to N00 E179. None of these lines reach to either pole. Whether you want to count that as 178 lines or just 89 lines I will leave up to you.
All caches should take a name in the format "Symmetry [bit1] [bit2]".
For lines in the Northern hemisphere that cross the Meridian, [bit1] is the latitude where the line intersects with the Meridian. I.e. N00 to N89. Similarly for lines in the Southern hemisphere that cross the Meridian. I.e. S00 to S89. The other lines should be named for the longitude where they cross the Equator. I.e. W001 to W179 and E001 to E179.
[bit2] consists of two (or possibly three) initials that uniquely identifies the cacher setting the cache, plus a number to distinguish between the caches set by the same cacher within the series (stating at "1" and incrementing by 1 for each cache placed).
Thus the name for my first contribution to the series I now look after is Symmetry N51 BH1.
If you intend to place a cache on this line, within the UK, then I would appreciate you letting me (BaSHful) know. This ensures that the bookmark list is kept up to date and also that there is no duplications of names, though that is not likely!
You are very welcome to set further caches on any of the other lines of symmetry. There is, however, no requirement to let me know. My interest is limited to Symmetry 51 within the UK. However, should you contact me, I may record your efforts here. No promises though!
I am aware of one cache, set by heartstones1.