***[Die][1]*** is the singular of ***dice***.

>***dice*** or ***die***
A small cube with each side having a different number of spots on it, ranging from one to six, thrown and used in gambling and other games involving chance.

Here is a passage explaining the confusing phrase:
> What did Jefferson mean by the obscure phrase "might want no fact of distinguished die." For "die" think the singular of "dice," which was correct usage as early as my childhood, in the 1950's. Think of how a whittler would make such a die in 1776. He'd use a long stick that he could easily strap down, and carve five facets on the free end (is "fact" singular for, or a misprint of the singular of "facets"?). Then he would separate (distinguish) the die from the stick, and finish the job on the sixth facet. To want no fact of distinguished di[c]e, then, is a metaphor for completeness. The case is stronger if we think the king's assemblage of horrors comprised five offenses before listing the promotion of slavery, an arguable reading. 

> [here](http://www.lectorprep.org/jefferson_and_slavery.html)


  [1]: http://www.oxforddictionaries.com/us/definition/american_english/die