Even if it is legal, I would only use "dice" in a plural sense,
because either the plural sense definition appears before the singular
definition, or most of the examples for "dice" are plural, and
because of the fact that "die" is specifically listed as the singular
of "dice":
http://dictionary.reference.com/browse/dice
http://www.thefreedictionary.com/dice
http://www.oxforddictionaries.com/us/definition/american_english/dice
The problem is that according to the Oxford dictionary, "dice" can be interpreted
either as singular or plural, making the definition ambiguous.
If the reader knows the sentences are written in Modern Standard English,
using the word "one" before "dice" could resolve the problem.
How would the reader know the sentences are Modern Standard English and
were not written before the time when this became a standard, or know that
the sentences didn't contain older references?
In this sentence, dice is not ambiguous because of the word "one":
"We lost one dice whilst playing the game yesterday."
However, in the following sentence:
"We lost dice whilst playing the game yesterday."
This sentence could be also interpreted to mean that "we lost
one (pair of) dice", E.G. that you actually lost 2 dice.
Even though this usage is valid according to the dictionary,
without the use of the word "one", anyone who has seen the word "die"
used as the singular or found a dictionary entry listing "die" as the singular
will have to guess as to whether "dice" is being used in the singular
or plural sense.
In this sentence:
"The 3D artist was developing a dice model, to be printed later."
The word "a" before "dice model" suggests that there is only one
actual model to be printed, but it's not clear whether a dice model
refers to one model of only one die, or to one model of multiple dice.
Could either of these sentences be used?
"The 3D artist was developing a model of only one die, to be printed later."
"The 3D artist was developing a model of (two, three) dice, to be printed later."