* πεπτωκώς (peptokōs): This is the perfect participle of πίπτω (píptō), meaning "to fall." It indicates a state of having fallen, and often implies a completed action with lasting consequences.
* πεσών (pesōn): This is the aorist participle of πίπτω (píptō), meaning "to fall." It emphasizes the single act of falling.
* ἑαλωκώς (healōkōs): This is the perfect participle of ἁλίσκομαι (halískōmai), meaning "to be captured" or "to be taken." This would be appropriate if "fallen" refers to being defeated in battle or being overcome.
* πτωμα (ptōma): This is a noun meaning "corpse" or "something that has fallen." This is suitable if you're referring to something that has fallen and is now lying down, perhaps lifeless.
To choose the most accurate word, you need to specify what has fallen and in what context.