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A Stewart Coffin original

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