I have a couple of D4s but both are lightweight and difficult to pick up, so I invented my own version (with help from Adrian Rossiter, Robert Austin and Vincent at the Magic Shop).
I believe the die to be a fair, as each of the pentagons joins two others and three trapeziums (one base and two side edges).
There is more info here... http://www.shapeways.com/
That's pretty cool. And shapeways.com appears to be a pretty good resource to be aware of.
Using pentagons is an unique choice. How did you reach that decision?
Luck, or logic?
Why did you choose, not to use an altered d8?
Or any other alternate version to the d4?
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I came across it by accident, fooling around with Jovo Construction, by joining together and enclosing four regular pentagons. The voids were later found out to be golden ratio trapeziums by Robert Austin and his friends, who took some time to document it. Adrian Rossiter at Antiprism and Vincent at the ‘Magic Shop’ (Shapeways) also contributed.
I could have used an altered D8 but this is something I can call my own. The numbering of the die is laid out differently as well.