AtaraxiA: a state of freedom from emotional disturbance and anxiety; tranquillity. Though both AtaraxiA's are disturbed in Imag-E, they later become places of peace.
There are two locations by the name of AtaraxiA in Imag-E. One is a planet on which Lord Mizer was first raised until he was about 6. Then Tohshaka took it over after he fled Mecuriel's Fraternity and restored Mizer's family mansion as his own. There is several beaches and a lot of wildlife on that planet. Although at one point there was a small town of angels with a small castle. Tohshaka relocates those angels to his small heaven in the sky (who later go to Ellipocene's heaven) after he rescues them from Daryk and Calintz.
The other AtaraxiA is the last island of Heaven and Hell, populated with mostly dense forests and seperated furthest from the rest. The island goes unused for many decades, although Kazumi and Toh later first discover it's Mecuriel's main hideout and has been since his first fraternity location collapsed due to Toh's earlier wreckage. The island is blocked off by a class 9+ cursed shield until Toh, Christopher's jet missles and Neao's dragon Ryu damage the shield enough to gain entrance. After Mecuriel is destroyed, Rio and Christopher later return to destroy his high tech castle, restore the further ruined buildings and angels slowly repopulate it as a normal island once again.