Three days remain until Flatland’s year-3000 celebration. A Square, Martin Sheen the attorney at law, struggles to instruct his son, A Hexagon, Kristen Bell, in the art of sight recognition. Their routine is interrupted when B, Joe Estevez Abbott Square, a clerk to President Circle, warns him to stay home during a Senate meeting. The session has been convened to debate the rising tensions between the government and the Chromatist movement, which seeks to let Flatlanders color themselves as they wish. The Great Southern Republic frames itself as democratic and distinct from the Northern Kingdom, arguing for open political reforms while fearing the consequences of appearing weak to neighboring powers.
Against his brother’s warning, A Square takes on a new client—the first woman charged as a Chromatist—sparking tension as he navigates a city already on edge. On his way home, he is caught in a riot that erupts in the streets after President Circle’s soldiers clash with Chromatist supporters. He makes it back to his house just in time to barricade his family and wait through the night, the city outside slipping toward chaos.
When morning comes, A Square learns that the riot originated in the Senate meeting that B Square attended. Martial law tightens its grip on the city as he hunts for his brother and tries to protect his loved ones. The tension escalates dramatically with the sudden appearance of A Sphere, Michael York the CEO of Messiah, Inc., who has chosen A Square to carry a radical message beyond Flatland: the existence of the three-dimensional Spaceland. A Sphere plucks A Square out of Flatland and into a realm that challenges everything he knows about geometry, gravity, and perception.
Together they travel to the Great Hall, where A Sphere explains the idea of three dimensions to President Circle and the Priests, who react with hostility and skepticism. When the Flatland leadership rejects the gospel and attempts to kill him, those who witnessed the event are executed, save for B Square, who is imprisoned for life on the condition of his silence. Realizing time in Spaceland may be limited, A Sphere transports A Square to Messiah, Inc. to deepen his education on the “gospel of Three Dimensions.” Enthralled by the new world, A Square begins to wonder if higher dimensions beyond three might exist, a notion A Sphere dismisses as dangerous speculation.
Meanwhile, A Square’s intrusion into Spaceland becomes a national emergency, prompting the Spaceland Senate to demand an explanation for the breach of protocol that brought a Flatlander into their realm. They warn that the incident could be construed as an act of war by their enemies, the X-Axis. A Square learns that the X-Axis regards Flatland as an abomination and seeks its destruction in the name of their own beliefs. As debate rages, the ailing A Square tries to articulate a theory of multiple dimensions to a crowd that remains unconvinced; air-raid sirens wail as the stress of gravity bears down on his two-dimensional body, and chaos erupts around him.
A Sphere manages to return A Square to Flatland just as Messiah, Inc. comes under attack. Back in his own world, A Square awakens to find that preaching about a third dimension has been made illegal. He discovers B Square jailed, and when he pleads with him to listen to the spacelike gospel, B Square resists, fearing execution and knocking A Square unconscious to protect him. The family plans to escape to the Northern Kingdom, seeking a place where they might speak more freely. They flee with the help of Frau A Square’s battle cry, a surprise tactic that helps them reach the border as the Northern Kingdom’s army moves to assist them.
The border clashes intensify, and as soldiers fire and chaos erupts, Flatland itself begins to fade away. In the final moment, as the world dissolves around him, a voice seems to welcome A Square into another dimension, suggesting that some realities lie beyond the limits of Flatland—and that the story may not be over.
