I think you might overlapping two concepts here. You see, there are things called "fragments" which were left by the gods that favoured Asterion.
Hades - Statue/Garden
Hestia - Mirror
Dionysus - Wine
Poseidon - (Incomplete) Sea
Hermes - The bedrock
Hera - ???
The other punishments you mentioned, are mere characteristics of the Labyrinth as stated in the constitution.
That's what I think though.