So, my colony mothership crawls along through sub-space at a "slow" ftl as it sends out faster probes ahead of it. Once it has located a cluster (meaning an acceptably dense grouping, not necessarily an actual star cluster) of worlds with "acceptable habitability" ratings (either habitable or can house stable enclosed colonies and have potential for possible eventual terraforming), it parks itself in the center of its selected region of space and then divides the space around it into "sectors", at least 8 of which contain at least 1 of the identified worlds. It then starts waking command crew for smaller colony ships to disperse in waves to each of these sectors.
My question is: what shape/angle should I make these "sectors"?
The outer radius of the "sectors" from the mothership is 1,000 ly (maximum 2-way distance for the ship's probes, which act as communications shuttles after colonization begins)
They need to (edited as actual shape is not required) allow the AI controlled mothership to use as a grid/array to organize, control, and monitor the colonization effort.
The sector size does not need to be large enough for the sphere to only house the 8 primary habitation sectors. It can include "dead" sectors of empty space or uninhabitable systems. However, each sector unofficially becomes the initial colony's "territory" for expansion, resources, and protection. As this is for a colony/empire control style game, they should be large enough that an ftl capable faction can establish a reasonable power-base and there still be room (at least on the outer/broader section of the sector) that most or all of the colonies are still exploring their sector, with only the ring around the mothership being very "crowded" space.
For conceptualizing: The probes and non-mothership vessels use an ftl drive that allows jumps of only a few hours between nearby (10-50 ly) systems, but can only maintain those speeds for a few jumps before needing resupply.
The mothership's support helps new colonies rapidly establish themselves to the point of being able to construct their own space craft (within about 20 years), and maintains a "carrier pigeon" transport that carries resources back and forth at regular intervals until then. Most are able to start establishing in-system mining operations and exploring neighboring systems within 30 years. First wave factions develop warships due to disputes over narrow trade lanes near the mothership and have warfleets protecting their territory by the end of the first century.
So, the goal is for "inner space" (meaning the region within 100 ly of the mothership) to be very metropolitan, highly populated and sometimes hotly disputed. The middle area (where the majority of the habitable worlds reside) is "civil space", each sector pretty much exclusively controlled by one faction. The outer edges of the sphere are still "frontier space" with mostly exploration expeditions, private prospecting efforts, and criminal havens separated by lots and lots of empty space.
The game begins as humans are starting to figure out what sort of neighborhood they landed in. Not that it has much bearing on the question, but the AI selected an area where its probes found no active interstellar civilizations out to their radius. So, at least through the establishment of its sectors, existing political boundaries were not considered.
When initially brainstorming the ship's process, the "sector" map was quickly sketched in 2d for conceptualizing purposes and we moved on to other things. I'm making a retro pass over things and hate the "orange slice" effect that putting the 2d map straight into a 3d universe would do. However, I won't have access to a decent ball of 3d playdough for at least 3 days. Help me out?
Edit: this is for a 3D video game, so the map perspective will be quite adjustable by the player.