Is a cross specifically used for stereocenter representation?
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According to IUPAC it is not incorrect for using it to depict carbohydrates being stereogenic or not. However here is an excerpt from the link listed below:
The use of Fischer projections in non-carbohydrates is problematic. Any drawings of this type are necessarily ambiguous since it is unclear whether the author of the drawing intended to make a Fischer projection or simply happened to draw a diagram in that orientation. Molecules depicted in the style of Fischer projections are likely to be recognized as such when they contain at least two acyclic stereo- genic centers oriented vertically, although such interpretation is not guaranteed. Molecules containing a single stereogenic center pose even greater problems since it is often convenient to separate the four ligands by equal angles whether or not a single stereoisomer is intended. Accordingly, although Fischer projections of carbohydrates are acceptable, similar depictions of non-carbohydrates should be used only when the viewer of the diagram is certain to understand that the diagram was intended to represent a Fischer projection. Fischer projections should be avoided where ambiguity is possible, including when used in computer applications.
See more here (page 37-38):