X≠Y≠Z: Three Body Problem

Our three body problem’s a bit of a riddle
Though our moods be discordant together we cling
Our center is everywhere and circumference the middle

We’re like Efimov dolls or a Borromean ring
Trinity’s not right, syzygy’s too twee
We won’t hum in pairs but as a trio we sing.

What’s your decree? What’s our wee rule of three?
(Though you should be aware we burn to Vern’s fiddle)
X is not Y and neither is Z.