Short answers, pulled from the story.
Polygon Magic emerged as a Japanese video game developer focused on arcade, console, and mobile platforms. The studio established itself by creating titles for various systems including the Nintendo Wii, Nintendo DS, and Nintendo 3DS.
Fighter's Impact arrived in arcades during 1996 to kickstart the studio's public presence. This title marked the beginning of continuous output across multiple hardware generations spanning over a decade.
Tsuri Sta appeared on GREE in 2008 published by the network itself while Sengoku Kingdom arrived on GREE in 2011. Polygon Magic helped GREE develop their first party titles starting around 2008.
Incredible Crisis remains one of the studio's most recognized works within the action-adventure genre alongside the Galerians series. Galerians released for PlayStation in 1999 while its sequel Galerians: Ash launched for PlayStation 2 in 2002.
Pachinko machines received their own custom software from this company. The studio produced games for Facebook and Japanese social networks like GREE and mobage before shifting focus entirely to mobile social networks.