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Frank,

I personally had not heard of the Diamond Cross or maybe just forgot. The Wikipedia article you reference seems to be a bit misleading.  It says "These four bright stars create an almost perfect diamond shape...It bears a striking resemblance to Crux". That's all quite a stretch. Being a perfect diamond would make it pretty hard to mistake for the distinct kit shape of the Southern Cross. Three of the 4 stars it contains are around 3rd magnitude so it's hardly very "striking". The Southern Cross and False Cross are very similar shapes and orientations with the the False Cross being slightly larger. Most locals know the you can tell them apart by looking for ε Crucis. The Aussies even put it on their flag,

Regards,
Robin