The statement below is false.
The statement above is correct.
The same shape indicate that the minis use the same die but which one ist not clear. Why does the pentagon mean d8?
Have a look at the dice sides.
Square for a cube (d6)
Each side of a d8 is a triangle
Each side of a d12 is a pentagon
The d10's sides are less regular, but the similarity is there, too.
But of course, your colors make things even clearer.
(Edit, doh, the d8's associated shape is indeed odd. Strange, I thought it'd make more sense - certainly did for me during play, strangely enough.)