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I'm having a bit of trouble grasping sugar stereochemistry.

Using glucose as an example, if you cyclize D and L glucose, is the stereochemistry at every carbon just inverted from the other form?

Like for example, on carbon 2 for D glucose, the hydroxyl is down. On carbon 2 for L glucose, the hydroxyl would be up.

Is this trend true for every hydroxyl or $\ce{CH2OH}$ group except the one on the anomeric carbon?

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Glucose is the hexose that projects its hydroxyl groups at positions C2, C3 and C4 as well as its CH2OH off C6 in the equatorial direction (in its low energy conformer that is). In the β and α configurations, its anomeric carbon C1 projects the hydroxyl in the equatorial and axial direction, respectively.

The D and L forms are mirror images in which all anomeric carbons have the opposite configuration between the two forms as:
glucose

Here are the equivalent structures using the Haworth projection.
Glucose

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