Yesterday it occurred to me that the multiplicative prefixes in the names of the Catalan solids (the duals of the Archimedean solids) are a pretty rare occurrence of those in traditional terminology, and would provide a good introductory illustration of their use in SDN.

The tetrahedrals and octahedrals work wonderfully:

triakistetrahedron =

**trinatetra**hedron (3*4=10) [sic; my mistake, should be

**trinaquadra**hedron]

rhombic dodecahedron = rhombic unquahedron

triakisoctahedron =

**trinanocta**hedron (3*8=20)

tetrakishexahedron =

**quadrahexa**hedron (4*6=20)

deltoidal icositetrahedron = deltoidal binunquahedron

disdyakisdodecahedron, hexakisoctahedron =

**binabinunqua**hedron (2*2*10),

**hexanocta**hedron (6*8=40)

pentagonal icositetrahedron = pentagonal binunquahedron

But there is a little problem with the icosahedrals, being that we see both "pentakisdodeca-" and "hexeconta-" as prefixes: the first means 5*10 (five faces corresponding to one of the regular dodecahedron), and the second just means 50. In the obvious SDN transform these both become

**pentanunqua-**and the distinction is lost. (So kind of like the traditional additive distinction between

**triacontakaidi**gon and

**triacontadi**gon.)

Perhaps we might then suggest that if there is any distinction between multiplication and a simple number, like in these names, or in base names (base 5-on-10 or pure base 50?), then we should instead use the

**nil**forms. This means that we might have to edit a few of the octahedral Catalan names:

icositetrahedron = binilihedron

And then we can finish up the job:

rhombic triacontahedron = rhombic bihexahedron

triakisicosahedron =

**trinanunocta**hedron (3*18=50)

pentakisdodecahedron =

**pentanunqua**hedron (5*10=50)

deltoidal hexecontahedron = deltoidal

**pentnili**hedron

disdyakistriacontahedron, hexakisicosahedron =

**binabinabihexa**hedron (2*2*26=a0),

**hexanunocta**hedron (6*18=a0)

pentagonal hexecontahedron = pentagonal

**pentnili**hedron

I think I much prefer "hexanoctahedron" and "hexanunoctahedron" to the other names with the repeated "bina". (It comes from the fact that the faces being atopped with pyramids are not regular; indeed they are the rhombi of the rhombic unquahedron and rhombic bihexahedron.)

I guess this would work, except that I am not sure which form feels more natural in dozenal for a number like 50, which is a multiple of the dozen. I don't think I feel the multiplicativeness inherent in it much more strongly than in "hexeconta-" in decimal; it fades into the background as it is inherent in the base. So the "pentnili-" forms seem slightly odd to me, as though they are telling me something, and only then is the multiplicativeness of "pentanunqua-" revealed. But I can't very well reverse things because the multiplicativeness is at least more present in "pentanunqua-" than in "pentnili-".

So I'm not sure what best to do here, even though this system seems to work, to distinguish a "five-times-dozen-hedron" from a "five-dozen-hedron" in SDN.

OP's edit: I changed the original title of this thread to better match what its topic ended up moving to. The original was: "Multiplicative SDN prefixes: Five dozen or five times dozen?".