I imagine Euclidian reproduction to work as follows.
As a note, reproduction is possible regardless of gender, but the process follows three stages. Fertilization, Separation, and Incubation.
The Fertilization stage begins when the pair slowly blend and fuse genetic cells from different points of their shapes. Pressing themselves together, usually at a point or corner. Growing the connecting section gradually until a new shape is clearly outlined from the combination of their DNA (resulting in the joined section being a different color). This process can take several hours and is uncomfortable and taxing for both individuals, there is very little "pleasure" involved and given the required focus of conjoining. Accidental births are not possible, it has to be intentional. Once the two Euclidians have successfully conjoined an outlined shape between them, the "Fertilization" stage is complete.
Afterwards the suggested protocol is to rest given the strenuous process of the previous stage, which also gives the fused genetics time to stabilize. Some however will rush the "birth" by immediately beginning Separation, tearing themselves free from the conjunction to leave an intact and newly formed shape. The gaps in their own bodies will eventually regenerate and heal (much like a starfish losing a limb). How long this takes will be dependent on each individuals health.
Finally comes the Incubation stage, as the new "baby" is not yet conscious and is more equivalent to an egg. After a gestational period where the parents will protect and nurture their offspring, creating a bond over several "months". The new shape will develop facial features such as eyes, internal organs and other necessary adaptations to conscious life. Becoming a brand new Euclidian that will grow up to eventually, if the right partner and conditions are met. Have children of their own.
Inspired by art by @akubaras-gf-au-collection
