There is a link to Slice&Dice's steam page in the description, this game is basically a tribute
About 20 days late to this but there are 27 dice:
3 basic dice, Fighter Rogue and Mage
6 Tier two dice, created by combing basic dice (order matters, example Fighter added to Rogue is Dancer, but Rogue to Fighter is ranger)
18 Tier three dice, created by adding a basic dice to a tier two dice (6 tier twos times three upgrade paths for each is 18 tier threes)
Making for a total of 27 dice. Now how many were actually designed by the creator and how many come from Slice and Dice, only Jorel can answer. (I definitely didn't misinterpret this question as you asking how many dice there were in the game :P)