Type of plants which have their points (5)

I believe the answer is:

cacti

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'type of plants' is the definition.

I don't understand the remainder of the clue.

(Other definitions for cacti that I've seen before include "Plants of dry regions" , "Prickly types" , "Spiny desert plants" , "Spiny succulents" , "Tough plants" .)

I've seen this clue in The Globe and Mail.

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