StryderNot entirely sure where you are going with your reasoning,
First part was in reference to question of "why do we age".
however I will state that I considered using the volume of a Dodecahedron for the base volume used in simulation.
I jumped from a total of 12 codons to 12 close-packed spheres by way of numerical association.
Codons = a threeness( triangulated association ), and 6( hex ergo hexagon of which the VE has four ) on each end of the chromatoid/nucleotide total to 12.
The 12 relates to the VE/cubo-octahedron ergo the basis of cosmic/generalized holographi scenario, that I believe is related to black hole phenomena and the basic blueprint for all complex biologicals( see more on that below )
I did not mention a "dodecahedron", but you appear to have gone off on a numerical association to 12 spheres association--- relates to
partial-space set --- to that of
all-space close-packing that relate to a the close-packing of Rhombic-Dodecahdra.
However, you then go off on 2ndary tangent by stating "pentagonal" so I think your perhaps confusing two differrent kinds of dodecahedra;
1) rhombic-dodecahedron( Archimedes polyhedron ) = 12 stable diamond/rhombic faces--all-space filling and more directly related to my stated VE/cubo-octahedron,
2) pentagonal dodecahedron( Platonic polyhedron ) = 12 non-stable pentagonal faces
The reason for using such a volume was the consideration of the inversed partnership of pentagonal faces (Consider mapping a Cartesian grid to one face based upon it's orientation, you'll find vertices partnered with a negative version on the other face), the fact that you can stack many dodecahedron together without spacing (and the stacking only works one particular way, cubes could be stacked irregularly) and the fact that dodecahedron's can have many different types of cross-sectioning that can be used alone or together with other symmetrical cross-sections to generate symmetrical objects. (It would make more sense when looking at 3D modelling, like for instance creating a lamp from a polar axis and using one 2D cross-section or the process of "translating" an object)
Again, you appear to be convoluting/confusing two kinds of dodecahedra above. Rhombic( not stated by you) "dodecahedron" and "pentagonal".
Sure both are related to numerical 12 by association, but do not have the more cosmic/generalized significance that a Vector Equlirbrium/cubo(6)-octa(8)hedron does.
The Euclidan( less spherical ) version of the VE/cubo-octahedron can be contructed using a wooden dowel and elastic tubing and since it has both regular squares it is both transformable and has a stable configurations as well.
This latter toy-like model is called a by its inventor( Bucky Fuller ) a 'jitterbug' and will fold into many spatial configurations;
1) Euclidean version of double-sine wave as commonly used to expression of EMRadiation,
2) negative saddle-shape space also found on torus,
3) from the above double-sine wave, the jitterbug will easily transform into basic quadra-pedic-like pattern of whales( mammals ) and fish;
..whales have their side appendages( fins? ) parrallel to their tail flukes orientation,
..fish have there side fins( appendages ) perpendicular to the tail fins orientation
..double-sine wave orientation is a combination of both of these above,
the list goes on for more spatial configurations that jitterbug will transform into, but these above are were of most significance in associations with biological patterning aspects. imho.
As for 2D graphing of 3D volumes, the 5-fold icosahedron and another polyhedron--- I forget the name of ---more efficiently transform 3D to 2D mapping.
However, niether of these have the inherent set of bisecting planes whose area is equal to the surface area equal to the sphere they define as does the VE-cubo-octahedron I mentioned originally.
Area quantity simulation via inherent geometries that define the polyhedron is best if not only possible via the VE/cubo-octahedron.
Least distortion of shape is in going from 3D to 2D mappiong, is best via icosahedron and one or two others I forget the names of.
r6