Of course, simple geometric shapes can be symmetrical along two orthogonal axes. A circle, for instance. Or ovals, squares and rectangles. Grilles with these shapes can be found -- especially the non-circle variety.
But the 1940 Dodge grille does not have a simple outline. That, and the segment dividers are what make unique, or nearly so.
Just for scene-setting fun, here is an advertising spread illustrated by Arthur Radebaugh (1906-1974), a guy who made many World of Tomorrow type images from the 1930s into the 1960s.
And here is what seems to be a factory photo of a '40 Dodge.
Now for that grille. There is side-to-side symmetry if the axis of rotation is the prow of the car. That is, the left and right sides have the same two-dimensional design. Most automobile grilles can make this claim. But then there is that painted metal running across the middle of the grille. The parts above and below it (again from a two-dimensional, flattened perspective) can be pivoted on that axis bar. This and the non-geometric outline of the grille are the unusual features. Photo from Mecum auctions.
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