firstly, cheers for making me think more tom

secondly, garthy is right about origin.
i remember i did a polyrhythm workshop at ejc once and this move appeared on my radar the following day.
my memory has recovered itself a bit and it was indeed ronan that first manifested this pattern at the ejc in ireland.
garthy later showed it to me and said something like "you know that 2:1 butterfly with one longarm circle and the other poi doing two wrist circles? if you keep your hands together, you get this thing instead".
so it probably is 2:1 after all.
well done tom

but damn if this area of poi isn't confusing at the moment.
Written by: nx?
its still polyrythmic even if the distance traveled is the same, because the rythum comes from the poi hitting the top/bottom of its arc (or other arbitrary point, as long as you measure by the same point each time).
yepyepyep - that's a great way to define a polyrhythm pattern.
slight disclaimer: agreeing with this point means i don't have to rewrite my polyrhythm thread so i may be slightly biased 
Written by: nx?
So the longarm circle hits top and botto once each per round while the trifoil has two 'circles' (things like this get veeera confusing in antis-pain).
this is true and its exactly why i think the overall counting systems are flawed and thus are only useful in certain situations - or should i say 'contexts'? 
count a 4-petal normal spin (i.e. same direction arms and poi) flower with beats at the bottoms of each arc and your beat count is 5.
count a 4-petal antispin flower like this and your beat count will be 3.
do a goofy flower like this and do you have a polyrhythm?
well that's the burning question ain't it...
beats are called beats because they describe a rhythm.
the reason beats are a useful tool is because you can count them off, in a steady rhythm, to help understand where your hands and poi should be at a particular point in a pattern.
if they described 'completed arcs' or whatever, we would have called them 'arcs' in the first place (and taken a lot longer to learn all the basic moves and even longer to understand them).
the old "one beat for every time the poi rotates 360 degrees" counting system has its place but there are places where it just doesn't cut it any more.
as soon as you find yourself with different or multiple points of rotation in the same pattern, that system falls apart completely and gives nonsensical counts for, what should be, easily described patterns.
nick found a good way to count 'compound circle' patterns ( i.e. fountains, flowers or any other pattern that mixes shoulder circles with wrist circles) a little while back: count every time the poi pass the centre point of the large circle (or every time the poi pass your arms).
with this counting system applied to the 4-petal flowers we were counting earlier, we get a count of 4 for both the normal and antispin versions.
the reason for this is that it removes the addition to or subtraction from the wrist circle count that the rotation about the shoulder contributes.
but this system is not applicable to patterns that mix epicyclic (antispin) and normal (extended circle) motions - to understand these types of patterns, we have to account for both points of rotation and their overall contribution to the pattern.
i.e. go back to the oldschool beat count of 'beats at 6 o'clock'.
take the example of the 4-petal flower once again:
with both poi antispin or both poi normal spin, you can count four equally spaced 'beats' using nick's system.
but reverse just one of the poi directions and the rhythm doesn't fit any more.
to keep the rhythm steady and at a count of 4 before the pattern repeats, you have to either slow down the antispin poi or speed up the normalspin poi.
i.e. to make a goofy flower a 1:1 pattern in terms of loops:circles requires that the poi spin at different speeds - its not the 'natural' pattern any more.
5:3 is the natural pattern in terms of compound circle beats (i.e. counting as they pass your arms).
but if you add the big circles and the little circle together, you get 4:4 - which is 1:1 again.
anyone understand that?
good.
talk to me about it one day and i'll get even more twisted and indecisive about which frame of reference we should take our count from depending on relative poi direction and number of centres of rotation required for the move.
until then i'm going back to my corner to hum and rock some more... 
cole. x