Welcome to the forum.
A lot of names are technical because it's mainly mathematicians who study it. A lot of the mathematical terminology crosses the natural meanings of words, which makes the subject somewhat more confusing.
We do have, eg 'polychoron' as being largely established opposite polyhedron.
I did a fair bit on this line in the polygloss, which does deal with the idea from an etymological view as well, largely because i needed a termonology that makes sense in six dimensions.
http://www.geocities.com/os2fan2/gloss/index.html
Not many of the figures, even in 3d have names. For example, the dodecahedron can be applied to any of the polyhedra with 12 sides. In fact the "decagonal prism" is a more precise term, since it refers only to a certian figure.
In higher dimensions, the ideas greatly spread out and grow, so it is rather a matter of finding a regular terminology for all of this.
I use several number systems (10, 120), so the idea of using numbers for names (eg fifhundchoron), is a matter of also selecting the base. Base 10 is less suited for this than other systems.
The cuboctahedron itself, is a figure that has two different reflexes in four dimensions (one with 20 vertices, the other with 24). The notion of 'vector equilibrum', branches into three or so parts in higher dimensions. Much is to be made of the role that the CO plays in 3d, because it is not replicated completely in any higher dimension (except, prehaps 5d and 8d).
Consider also, that there are many strange things in 4d that we have no way of seeing in 3d, such as the bicircular tegum, or the pentagon-pentagram tegum (which has 25 regular tetrahedra as faces).