Euclase, also known as Euc, is one of the elder Gems in the community, distinguished by a hardness of 7.5 on the Mohs scale. Their primary role within the group is that of a secretary and aide to Kongo-sensei, the enigmatic leader they all serve. In this capacity, Euclase is responsible for a wide array of administrative and strategic tasks, most notably managing the shift schedules for patrols and using their aptitude for calculations and predictions to anticipate when the Lunarians will attack.

In terms of personality, Euclase is defined by a calm, composed, and highly responsible nature. They take their duties as a secretary with the utmost seriousness, yet this professionalism is tempered by genuine kindness and a caring attitude toward all their fellow Gems. This is particularly evident in their interactions with younger or more troublesome Gems like Phosphophyllite, with whom they are willing to share jokes and offer patience. Euclase is also acutely perceptive, being one of the first to sense that something is amiss with Phosphophyllite's behavior following a return from the Moon.

A core aspect of Euclase's character is their reliance on reason and diplomacy over violence. They are well aware of their own limits and refrain from unnecessary or futile actions, preferring to seek solutions through logic and discussion. This preference for reasoned mediation defines their role in the story, particularly in the later stages when the Gem community faces an unprecedented crisis. While others are driven by anger, fear, or a thirst for battle, Euclase consistently advocates for a more measured and pragmatic path forward.

Euclase shares a close working relationship with Jade, who serves as the chairperson of the Gems. While Jade acts as a mediator, Euclase handles the secretarial work, and the two are frequently seen discussing strategies and the state of their society. Their bond with the leader, Kongo-sensei, evolves significantly. In a pivotal moment of turmoil, when many Gems are unable to process the truth about their situation, Euclase is the one who steps forward to address Sensei directly. They suggest beginning their relationship anew, proposing a future built on equality rather than servitude, demonstrating remarkable maturity and leadership.

Throughout the narrative, Euclase shows significant development, transitioning from a diligent administrator to a key decision-maker. When the community is fractured, Euclase prioritizes the group's stability. In a striking example, when Phosphophyllite is shattered into pieces, Euclase advocates for reassembling them in order to negotiate and find a non-violent resolution, even as others argue for scattering the parts to prevent further conflict. This action underscores their unwavering commitment to finding a path through dialogue, even when faced with immense difficulty.

Euclase’s notable abilities lie primarily in their intellect. Their talent for making accurate calculations and predictions is invaluable for organizing defenses against the Lunarians. While not a front-line combat specialist like some of their harder peers, Euclase is not averse to taking action when necessary, such as being among the first to rush to Phosphophyllite’s aid during an attack by a giant mollusk, even though their weapons proved ineffective.