Abarim Publications' online Biblical Hebrew Dictionary
Officially not related, the two words פה (ph) and פאה (p'h) show a remarkable consistency in usages:
There are two words in Hebrew that are spelled פה (peh), but they are probably unrelated:
The masculine noun פה (peh) means mouth. It's also spelled פו (pw) and פי (py). This noun shows up in cognate languages across the Semitic spectrum, and although scholars attest that it has no clear root or origin, here at Abarim Publications we find it pretty clear that it is either formally derived from or else popularly connectable to the verb פאה (pa'a), meaning to cleave (see below). In other words: the mouth is essentially a cleft.
The word פה (peh), meaning mouth is used in much the same fashion as the English word mouth is: as organ with which to eat and drink (Genesis 25:28, Judges 7:6), and as organ of speech (Genesis 45:12, 2 Samuel 1:16). This word is not limited to a human mouth; animals have them too (birds: Genesis 8:11; bear and lion: 1 Samuel 17:35), and God has a mouth as well (Isaiah 1:20, Jeremiah 9:11). Several inanimate items have mouths: a sword (its mouth is the edge of it, or perhaps rather the part that does the cleaving: Proverbs 5:4), a well (Genesis 29:2), a cave (Joshua 10:18), etcetera.
The suggestion that our noun may be derived from the verb פאה (pa'a) is made even more compelling by the use of our noun in the sense of extremity. The compound פה לפה (peh lepeh) means from one end (of the temple) to the other (2 Kings 10:21). And it may also serve to convey some measure or quality (perhaps serving as the 'name' of things that have no name): according to one's appetite (Exodus 16:21), according to the numbers of one's years (Leviticus 25:52).
Another word for mouth is חך (hek).
The adverb of location פה (poh) means here (Genesis 19:12, Numbers 22:8) or hither after a verb of motion (1 Samuel 16:11, Ezra 4:2). It's also spelled פו (po) or פא (p')
These two words are probably unrelated but the usage of פה (peh) in the sense of extremity, which is a locality, seems to suggest kinship with פה (poh), meaning here.
The verb פאה (pa'a), meaning to cleave or break apart, occurs only once in the Bible, namely in Deuteronomy 32:26, where just after the mention of a sword, YHWH exclaims, "I will chop them to pieces!" (which in Hebrew is presented by the single word אפאיהם). But from this verb comes the feminine noun פאה (pe'a), meaning corner or side. This noun occurs eighty-two times and mostly in a construct ( . . . -side, or side-of- . . . ). Half of this noun's occurrences are in the Book of Ezekiel, where it describes the sides or edges of the temple or parts thereof. Our word may also be used to describe the corner of a couch (Amos 3:12), a table (Exodus 25:26), a field (Leviticus 19:9) or a kingdom (Nehemiah 9:22).
The famous prohibition to strike off or round the corner of one's head or destroy the corner of one's beard gave rise to typically Jewish coiffure (Leviticus 19:27, 21:5), and this custom is generally explained to have to do with the habit of surrounding nations to somehow make markings in one's hair in order to delude spirits, and all that (see Jeremiah 9:26, 25:23, 49:32). But note that the word for hair does not occur in all these contexts, and the term "cutting the corner of one's head" may in fact be a colloquial expression of which the meaning has been lost.
Here at Abarim Publications we're more drawn towards the parallel with the decree that a man should not cut the corners of his field so that the poor and disenfranchised may help themselves to the surplus (Leviticus 19:9). We're guessing that the Lord wanted Israel to be a nation of people who nourished their properties but not at the cost of the less privileged, but instead as a means of caring for the less privileged. We're guessing that the idea of cutting the corner of one's head had more to do with hoarding than with hairdo.