Hi Brouhaha
Thanks for the data. Everything we need is there.
Are your LED's embodied in the sculpture already, or are you still at the experimental stage?
If you still have freedom to play with the arrangement, I would suggest splitting the LED's into two strings of six, each with a Dynaohm in series.
Taking the 'typical' figures, with 3.2V across each lamp, thats 19.2V across six, plus the drop across the Dynaohm of 2.6V = 21.8V so with a 24V supply it should work - BUT if we take 'worst case' of 3.5V across each lamp, that's 21V across all, plus 2.6V = 23.6V, rather close to your power supply output. That's why I think it's best to try it!
You can of course keep to your original scheme of having three strings, but with a smaller number of lamps in each string, I think it's a good idea to have a Dynaohm for each. I was just trying to save you having to buy more Dynaohm's than you need!
If you have a multimeter it would be useful to check you do get these voltages and currents in practice.
Finally I'm not clear why the bulbs should "blow up" unless you connect one the wrong way round, or directly across the supply!
I can see why some may not light when you have parallel strings of a small number of lamps - that's what you need to avoid.
Unless your Dynaohm has blown up while experimenting. It's vital you have a current limiting device like that in each circuit, otherwise you will destroy the bulbs connecting them straight to the psu.
It would be really useful to have a multimeter to check you have 20mA flowing through the Dynaohm(s).
Good luck with the project