OK, I realise this may be pedantry taken too far but I get annoyed everytime this is sung at playgroup and everyone makes a rhombus shape with their hands.
There is no such mathematical shape as a diamond. It is a rhombus, or perhaps a kite.
The song means the star is twinkling like a diamond.
This is probably why so many children turn up in my Year 7 maths classes thinking a rhombus is called a diamond.
And yes, I would be too embarrassed to mention this in RL.
Please be nice to me.