I researched several dictionaries and I am unable to precisely identify the term. Thank you.
They are called 「へり」 or 「畳{たたみ}(の)へり」.
The pitch accent is on the 「り」, which would mean that many J-learners would tend to pronounce the word incorrectly by placing the accent on the first syllable 「へ」.
It is 「[へり]{LH}」.
Put the accent on the 「へ」 and you will be saying the katakana word 「ヘリ」 meaning "helicopter" instead -- 「[ヘリ]{HL}」.
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1It's interesting that many japanese native speakers I speak to, complain that in english you sometimes change the pronunciation of a character, that it isnt't phonetic. But japanese itself also has it's own tricks when it comes to pronunciation, right? – Felipe Chaves de Oliveira Mar 9 '17 at 13:45