This sounds like it could be the book Children of Chaos by Dave Duncan
Here is a website for Dave Duncan detailing a single chapter and some reader reviews
On a dodecahedral world in thrall to the tyrannical, war-obsessed Hrag dynasty, no one could stop the Bloodlord from sending troops to Florengia, invading its major cities, and offering them a choice between strict colonial rule or immediate and total destruction. When the doge of Celebre was faced with this ultimatum, he gave his children up as hostages so that the rest of Celebre might live. Thus the four young Florengians were taken back over the Edge and scattered across the Vigaelian face.
Fifteen years later, when Celebre suddenly takes on crucial political significance, one of the siblings must return home to serve as Celebre's puppet ruler and the others must be eliminated so that there are no rival claimants to the throne. It's going to be tough enough finding each other, let alone deciding whether enough kinship remains after fifteen years apart that the siblings care enough to help each other out of their respective predicaments. If they're feeling particularly altruistic, the Celebres might even take on the bonus round: trying to save Dodec from the culture of death and war imposed on it by its evil warlords.
One thing's for certain: the Celebre children are going to have a lot of adjusting to do..
Taken from the Curled Up review of the book:
The eldest boy, Benard, is a warm-hearted, romantic artist who is also a favorite of his goddess, Anziel. The second boy, Orlando, is fanatically loyal to the Vigaelian leaders and wants nothing more than to be initiated into to the cult of Weru and kill the rebel Florengians. The girl Fabia has grown up as the pampered daughter of a rich merchant and has no knowledge of her roots. They live in different cities, unaware of the existence of the others.
- The siblings are heirs to a kingdom
- They are separated at birth
- One of the brothers is described as an artist, and the second as a warrior.
- There are four siblings who were given away
- The world is a dodecahedron