The spherindricites are a derivative of the tetrabrachs, brought about by a mutation that caused repeated cell divisions along the vertical axis prior to limb differentiation, resulting in an elongated (spherindrical) segmented body plan with varying numbers of tetrahedral segments, analogous to the segmented worms which gave rise to arthropods on Earth. The development of segmentation was quickly followed by evolution of invaginations in the body surface to increase surface volume; due to the much higher surface-to-bulk ratio of 4D organisms compared to the surface-to-volume ratios of similar 3D organisms, and the small maximum distance from any point on the interior of a tetrabrach to the surface, small tetrabrachs and early spherindricites had no need for any specialized breathing structures, as liquids and gasses could passively diffuse through the creature from the environment. However, surface pockets which would be alternately compressed and expanded by the creature's movement, thus getting the surface closer to some internal volumes and actively pumping fluid past them, allowed spherindricites to grow to much larger sizes.
The least derived spherindricites, which retain minimal differentiation between their segments, primarily occupy benthic and burrowing niches and are an exceptionally diverse group, just like their close Earthling analogs, the annelids, coming in a wide range of sizes and with a variety of reduced or specialized limb structures. However, one free-swimming group of spherindricites developed encephalization--the fusing and specialization of segments at the mouth end of the creature, which had transitioned from the bottom to the forward orientation, creating creatures with distinct heads and their fronts. The forwardmost set of limbs specialized as mouthparts for grabbing and manipulating food; two of the second-segment limbs specialized as olfactory sense organs, while the remaining two developed more advanced eyes from the terminal ocelli, with ocelli disappearing from the remaining limbs.
One group of cephalic spherindricites, the malakichthys ("soft fish") directly developed a new up-down axial symmetry breaking, with one limb from each body segment specialized as a dorsal stabilizing fin and the remaining three becoming propulsive limbs radially arranged in the sideways plane.
The remaining cephalic spherindricites developed internal mineral storage structures, which would serve as the basis for structural bones. This group further diverged based on three different approaches to developing their own secondary vertical orientation:
- Polysphenoids dropped two limbs from each body segment, resulting in alternating left/right and ana/kata-aligned limbs, such that the tips of each limb from any two adjacent segments form the vertices of a disphenoid.
- Trilaterians dropped a single limb per segment to allow planar compression, resulting in adjacent body segments forming alternating triangular antiprisms, with each set of limbs arranged in an equilateral triangle in the sideways plane.
- Quadrilaterians simply rearranged their four limbs per segment into a square arrangement in the sideways plane rather than a tetrahedron.
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