A writing kaomoji holds a pen to the page: in φ(..) the Greek letter phi is the pen and the two dots are eyes looking down. Wikipedia's list of emoticons gives that face as jotting a note.
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Writing text faces, by the tool held
A pen: the Greek letter phi and A pen: the closing mark 〆 draw the pen with a letter or a punctuation mark. A pencil in hand uses ✎, ✏ or ✐, and A fountain-pen nib uses ✒ or ✑. In (・_・)✎﹏﹏ the face has a wavy line on the page already.
Reading, and with a word
Reading sets a book in front of the face: [本] is a box around 本, Japanese for a book. The last group adds a word: メモ for a memo, 勉強 for studying, 宿題 for homework, 読書 for reading, 手紙 for a letter and 日記 for a diary, as Wiktionary gives them.
✏, ✒ and ✉ are on Unicode's emoji list; the note under a tile says so.
Questions and answers
What does φ mean in a kaomoji?
φ is the Greek small letter phi. In a kaomoji its upright stroke through a loop stands for a hand holding a pen, so φ(..) is someone writing with their eyes on the page.
Is there an emoticon writing a letter?
Yes. The group Writing a letter adds ✉, which Unicode names Envelope: φ(・ω・ )✉ has the pen in hand and the envelope waiting, and (・ω・)っ✉ hands the letter over.
What does a studying kaomoji look like?
Wikipedia's list of emoticons gives a face with a pen and a trail of dots as studying. Here that is ...φ(・∀・), and φ(・ω・ ) 勉強 adds the Japanese word for studying.
Why does a writing kaomoji show an empty box?
A device with no font for a character draws a box in its place. The pencils, nibs and envelope come from the Dingbats block of Unicode, and the words in the last group need a Japanese font.
All 60 faces
A pen: the Greek letter phi 14
( ..)φJotting a note, pen on the right
(・_・ )φPen on the right, eyes turned to it
...φ(・∀・)A trail of dots already written
_φ(・_・Hunched over the desk, bracket left open
φ(-_- )Eyes shut, still writing
φ(..)Jotting a note
φ(._. )Small eyes looking down
φ(>_< )Stuck on a hard one
φ(^_^ )Writing with a smile
φ(°-° )Wide eyes on the page
φ(・ω・ )Pen on the left, looking over at the page
φ(｀_´ )Brows down, pressing hard
φ(￣ー￣ )Flat eyes and a long flat mouth
φ(T_T )Tears over the page
A pen: the closing mark 〆 7
(・ω・ )〆Closing mark on the right
_〆(・ω・ )Pen to the desk line
〆(-_- )Eyes shut, signing off
〆(. . )Eyes down, closing mark in hand
〆(^_^ )Smiling, closing mark in hand
〆(・_・ )The closing mark held like a pen
〆(°o° )Mouth open, writing it down fast
Show all 60 faces (39 more)
A pencil in hand 10
(-_-)✎Eyes shut, pencil in hand
(. .)✎___Eyes down, three blanks to fill in
(>_<)✎Eyes screwed shut over the pencil
(^_^)✎Smiling, pencil in hand
(^ω^)✏A w smile and the level pencil. ✏ is on the emoji list.
(・_・)✎﹏﹏A wavy line already written
(・_・)✏The level pencil, held out. ✏ is on the emoji list.
(・ω・)✎A pencil held at the right
✐(^▽^)Pencil up, mouth open in a smile
✐(・ω・ )Pencil pointing up, at the left
A fountain-pen nib 7
(-ω-)✑Eyes shut, a white nib
(>_<)✒Eyes screwed shut, a blot coming. ✒ is on the emoji list.
(^_^)✒Smiling, nib in hand. ✒ is on the emoji list.
(°_°)✑Wide eyes and a white nib
(˘ω˘)✒Resting eyes, nib in hand. ✒ is on the emoji list.
(・_・)✒A black nib at the right. ✒ is on the emoji list.
✒(・ω・ )Nib at the left, a small w mouth. ✒ is on the emoji list.
Writing a letter 5
(^_^)✎ ✉Pencil and envelope. ✉ is on the emoji list.
(・ω・)っ✉Handing over a letter. ✉ is on the emoji list.
φ(-_- ) ✉✉✉Three envelopes still to go. ✉ is on the emoji list.
φ(・ω・ )✉Pen in hand, envelope waiting. ✉ is on the emoji list.
✉⊂(・ω・)Reaching for the envelope. ✉ is on the emoji list.