According to the fine folks at Puzzle World, "The Star of David is in the same family as the Diagonal Burr and its many variations made by Stewart. It uses six dissimilar and non-symmetrical pieces. This unusual puzzle assembles into three different geometrical shapes having an axis of symmetry, as well as other shapes having no apparent symmetry. A difficult puzzle. Stewart made 50 from 1981 to 1983 and 10 of a simpler version in 1990. Numbers 37 and 37A in his numbering system."

The next photograph shows the Star of David in one of its alternate symmetrical assemblies.

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top half

notice the numbers I penciled in the center -- 1 2 3 > (facing towards the right)

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bottom half

also notice the orientation of the numbers
(which way they're facing) -- < 4 5 6 (facing towards the left)

Orientation is crucial, otherwise assembly of the two halves will be impossible (except for the various combinations that are displayed below).

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top pieces

These next two photos depict the pieces as they're oriented for the Star of David's regular shape .

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bottom pieces

note: the angle brackets presented below, alongside the numbers,
denote the correct orientation of the pieces . . .

Different combinations that can be used for acquiring various shapes are :
123> --- <465 regular shape
<135 --- 264> chaos
<123 --- 456> drooped sides
<123 --- 465> crushed top / sliced side
<132 --- 465> sliced symmetry