It seems to me that most of the responses here are related to traditional additive i.e. a bank of sine waves that are tuned in set intervals, not too far from an electric organ. This is fine of course, but I thought I'd try to mention the Buchla approach.
The Buchla (and to some extent Serge) approach to additive synthesis was very much based on two oscillators combined with waveshapers (folders) that affected the timbre. Most people wouldn't think of this as additive synthesis but when you look at it closer it can be considered a form of additive synthesis.
Usually in the standard Buchla voice you have a modulating oscillator and a principal oscillator. These can function as either two separate oscillators but most commonly the modulating oscillator adds frequency content to the principal oscillator via i.e. frequency modulation. Then there is the timbre or wave folder section that is connected to the principal oscillator. A wave folder bascially ADDS harmonic content to i.e. a sine or a triangle by folding the wave in some way I don't know how to describe.
The modulation oscillator, principal oscillator, and the timbre are all part of the 259 (or 261e) Complex Waveform Generator.
There are variants of wave folding that allow more emphasis or odd or even harmonics. I really like the sound of wave folding, it sounds like something turning itself inside out and it's a big part of the Buchla sound imho.
I think the Buchla Easel is a really good "East Coast" equivalent to something like the Minimoog, although at the same time they are not comparable. The only way they are comparable is that if the Minimoog distilled the essence of subtractive synthesis from a modular system, the Easel could be viewed as having distilled the essence of a west coast type modular system into a smaller and more manageable format.
Finally I'm not sure it would be viable creating an analogue polyphonic instrument inspired by the Buchla philosophy due to how the different modules interact (I haven't accounted for the function generators or low pass gates, etc). Either most if would have to be done in DSP, or it would be increadibly expensive.
But if you want to get a feel for how a polyphonic buchla inspired instrument could sound, I can recommend the Madrona Labs AALTO plugin.