I had fun playing your game, but I wish there was a way to make more meaningful choices during combat. There is an obvious better way to play (just choose the highest dice), and no reason to do otherwise, which makes the fights a bit automatic. The only time you need to pay attention is when the enemies roll their best dice as the second or third, then you have to consciously keep your best dice for last. I'm not sure how you could make things a bit more interesting, but I encourage you to try my game to see how I tried to make dice based combat interesting (sorry for the shameless plug :D)
The dice shape world is a nice idea, but towards the end when there is only one or two fights left it's easy to get lost. Maybe indicating in which direction the next fights are would help, or removing the paths toward empty sides (or even making a magic dice where whichever path you take you end up where you need to go.)
I liked the heal mechanic, that's an interesting choice! Do I keep on going, risking my life, or do I start reroll the dice, having to fight again through all the fights, but stronger than my last attempt? That was clever!
A very good entry, that can become something really great with some tweaks!
P.S.: no dice in paradice! Unbelievable!