quickfur wrote:So the omnitruncated 600-cell, for example, would be the rhodopantome.
I think you mean
rhodopantomochoron, to distinguish it from the omnitruncated dodecahedron/icosahedron which would be the
rhodopantomohedron!
So let's see. Adopting your "meso-" for rectates (and using "dimeso-" for cantellates, since a cantellate can be obtained by rectifying twice), we now have the following for the uniform polyhedra (only missing snubs):
pyrohedron, pyrotomohedron
geohedron, geotomohedron, stauromesohedron, aerotomohedron, aerohedron, staurodimesohedron, stauropantomohedron
cosmohedron, cosmotomohedron, rhodomesohedron, hydrotomohedron, hydrohedron, rhododimesohedron, rhodopantomohedron
Alternatively, if we bring the prefix for the truncation type to the front, we get:
pyrohedron, tomopyrohedron
geohedron, tomogeohedron, mesostaurohedron, tomoaerohedron, aerohedron, dimesostaurohedron, pantomostaurohedron
cosmohedron, tomocosmohedron, mesorhodohedron, tomohydrohedron, hydrohedron, dimesorhodohedron, pantomorhodohedron
Although the second way is more analogous to what we currently do ("truncated"+"cube" => "tomo"+"geohedron", etc.), I think I prefer the first way (your way) when seeing them both together like that.
As for polychora, let's see what we can make (I'll only list the first way for these):
pyrochoron, pyrotomochoron, pyrotomichoron, pyromesochoron, pyrodimesochoron, pyropantomochoron
geochoron, geotomochoron, geotomichoron, stauromesochoron,
aerotomichoron (= 24-cell), aerotomochoron, aerochoron, staurodimesochoron, stauropantomochoron
xylochoron, xylotomochoron, xylotomichoron, xylomesochoron, xylodimesochoron, xylopantomochoron
cosmochoron, cosmotomochoron, cosmotomichoron, rhodomesochoron, hydrotomichoron, hydrotomochoron, hydrochoron, rhododimesochoron, rhodopantomochoron
I've omitted
Dx numbers 5, 7, 11, 10, 14, 13 (that is, cantellate, cantitruncate and runcitruncate, and those operations applied to the dual), which don't have a prefix yet.
I obtained
tomi- by combining
tomo with
hemicate, my word for the four-dimensional Dx 2.
It seems that the 4D cantellate (Dx 5) is equivalent to hemicating twice. So if
tomi- is used for Dx 2 then
ditomi- could be used for Dx 5. Then we'd have pyroditomichoron, geoditomichoron, xyloditomichoron, cosmoditomichoron and hydroditomichoron.
How's this look so far?