A Dice

The word dice is a plural word. People often mistakenly use the word dice to refer to a single die. Hence the expression 'the die has been cast' (a phrase with an interesting history) and not 'the dice ...'. However, I came across this interesting object in Vienna in November 2005 (although it seems to have been made in China). Here we have a die-within-a-die. So, in a sense, there is something singular about it. So might this be 'a' dice?

NB On both dice, the one and the four are represented by red spots, whereas all the other numbers are represented by black spots. I afraid don't know why.