does this insect belong to the Phasmatodea or the Mantodea?

Thanks for commenting & naming. Cheers, Sam.

I'd vote for the Praying Mantis based on the triangular head. Try feeding it...Mantids are carnivores and Mantodea are vegetarians. Maybe put out a salad plate and a bowl of fresh aphids. See which one he/she/it prefers. Of course after the first sentence, any further knowledge of mine about these insects plunges to zero. Was this on your ceiling?

William, thank youy very much for your input which follows the line I had set out for myself in determining the type. It's the triangular head indeed that gives its identity away &, in a detailed capture, the composition of the mouth which let me think it would be a carnivore instead of a vegetarian. Unfortunately, I couldn't quickly enough find a dish of juicy aphids to get our assumptions tested ;-) Cheers, Sam.