Sphynx

Sphynx (スフィンクス) is the pet calico cat of Index. First found by Index in the second volume of the Light Novels as an abandoned cat, it later becomes a constant companion to Index with one not often appearing without the other.

Appearance
Sphynx is a kitten, and as such is small and can be easily carried around by Index. In fact it is often seen inside of Index's Walking Church. Sphynx, like cats of its breed, is covered with patches of brown and black fur covering its white coat. Sphynx has yellow-green eyes and sports a red collar around its neck (after being taken in by Index).

Deep Blood Arc
Sphynx is first seen by Index inside a box after Touma and she finished eating in Macronall Hamburger and meeting Himegami Aisa. Index wanted to take in Sphynx, however, Touma rejects her request as it is against the rules in his dormitory to keep pets. Because of their arguing, Sphynx runs away, with Index trying to follow, however, she quickly discovers a mana source set up by Stiyl and runs off to investigate, leaving Touma alone who later meets Stiyl Magnus for the first time after the John's Pen Incident.

When Index and Touma come home, he discovers that Index has taken in Sphynx. Though reluctant at first, Touma allows Index to keep Sphynx and shortly leaves for Misawa Cram School with Stiyl. Index later takes a bath with Sphynx, and becoming suspicious of Touma's actions decides to find him, she eventually follows Stiyl's mana trail to Misawa Cram School, where she meets Aureolus Izzard, who makes her fall asleep.

Touma later realizes that Index may be in danger, as he discovers Sphynx with Index's hood near the school.

By the end of the arc, Index pays a visit to Touma in a certain hospital, bringing Sphynx along where it proceeds to scratch Touma's face.

Sisters Arc
In the time between the Deep Blood Arc and the Sisters Arc, Sphynx somehow acquired fleas, which led Index and Aisa to try find ways to get rid of it. When Touma comes home to his dormitory with Misaka 10032, he discovers that Index is going to use sage as a way to remove the fleas, while Aisa decided that she was going to use an insecticide spray to purge Sphynx of the fleas. Sphynx is later spared of their remedies when Misaka 10032 decides to intervene, by giving Sphynx a slight electric shock using her abilities to kill the fleas. The scene is slightly different in the manga version (since it skips the Deep Blood Arc), where Index just recently acquired Sphynx and Touma as well to his surprise, however, Misaka 10032 still shocks Sphynx in the end, with Index being highly impressed of her.

Three Stories Arc
The majority of the arc has Sphynx with Index, however, when she was kidnapped by Yamisaka Ouma, Sphynx was carried around by Touma until he saved Index. When Ouma, after receiving serious injuries from Index's grimoire he was about to give up when Touma used Sphynx to scratch him in the face before helping Ouma to cancel the curse that the woman is in love with was stricken, and is the reason he was after Index.

Kazakiri Hyouka Arc
Index carries Sphynx with her to find Touma, as she had no lunch. After meeting Kazakiri Hyouka and reuniting with Touma, Index allows Hyouka to play with Sphynx, she tries to hug Sphynx but is suffocated by her large breast size, as such Sphynx is deterred by her, to the lament of Hyouka.

Later, after being teleported by Shirai Kuroko when Sphynx was with Index. Sphynx runs away for some reason, forcing Index chase after Sphynx, because of this Sherry Cromwell's golem finds Index and attacks her.

In the anime ending of the 1st season, Sphynx mimics Index's facial expression when she discovers that Touma is eating something, when she was starving. Index later bites Touma as well as Sphynx.

Orsola Aquinas Rescue Arc
Sphynx is in the care of Tsuchimikado Maika after Stiyl 'kidnaps' Index to force Touma to get involved in his current mission to retrieve Orsola Aquinas and the Book of the Law.

Tree Diagram Remnant Arc
Sphynx appears briefly during this arc, here, Touma is cooking food for Sphynx while Index is asking questions to Touma about the weather reports. When Index notices Touma cooking food for Sphynx, she gets angry and bites Touma.

British Royal Family Arc
Sphynx was sent ahead on the supersonic plane to UK, and was taken in by Itsuwa who arrived to try and pick up Touma and Index but ended up with only Sphynx. Later, before Touma and company headed off to fight against Carissa in the climax of the civil war, Sphynx was seen trying to snatch food from various other nuns. After Touma and others have left, Riméa arrived at the place where Touma was, and took a liking to Sphynx and considered taking the cat in, much to her loyal pet dog's displeasure.

Sphynx was last seen with Riméa in the light novels, as of Volume 20. Presumably Riméa have taken Sphynx in temporarily after its owners (Touma and Index) are busy elsewhere.

Homecoming Arc
Sphynx is seen in volume 2 having been reunited with Index and returned to Academy City with her. When Touma returned, he noted that the cat appeared bigger than he remembered.

Magic God Othinus Arc
Despite the clear and present danger, Index brings along Sphynx with her when Touma leaves to deal with GREMLIN. It also bears witness to the end of the world after Othinus uses Gungnir.

Later, after Othinus remakes the world, Sphynx is present in both the Beta World and Omega World, always being carried by Index.

After the events of the manhunt for Othinus and Kamijou Touma has concluded, Sphynx is carried to Touma’s room in the Heaven Canceller's Hospital, where the depowered Othinus is also present, now in the form of 15 centimeter person. After Othinus explains why she survived the fairy spell that was killing her and why she had become so small, Sphynx attacks her, much to Othinus’ horror. Othinus is later seen dangling from Sphynx’s mouth carrying her like a fish as she reminiscence on her punishment given to her by the world.

Toaru Majutsu no Index: Love Letter Competition
Sphynx is with Index after they notice the Kumokawa Seria's "love letter" Kazakiri Hyouka delivered to Touma's dorm after a series of mishaps.

Shinyaku Toaru Majutsu no Index SS
Index brings Sphynx along with her in order to find a present for Touma that can make him happy. Due to Sphynx being a cat and the unique Egyptian name it has, it entices the magician Leep to use the cat to peak into Index’s mind to see if her desired copy of the Book of the Dead has been reconstructed inside of her, as she has discreetly shown clues to Index that would allow that to happen.

Sphynx and Index later return to Touma’s dorm safe sound after Index’s battle with the magician.

Toaru Majutsu no Index Movie: Miracle of Endymion
Index carries Sphynx with her during the beginning of the movie. The cat is with her in their meeting with Meigo Arisa. Later, after Arisa comes to after the attack on her by magicians, Sphynx cuddles with her, and later licks her tears as she delivers a monologue on how her voice causes bad things to happen. Index does not carry Sphynx later in the film, and presumably stays in Touma's for dorm for the rest of it.