Some Basic Results
The pretzel link is a knot iff both and all the are odd or exactly one of the is even.
The pretzel link is split if at least two of the are zero; but the converse is false.
The pretzel link is the mirror image of the pretzel link.
The pretzel link is link-equivalent (i.e. homotopy-equivalent in S3) to the pretzel link. Thus, too, the pretzel link is link-equivalent to the pretzel link.
The pretzel link is link-equivalent to the pretzel link. However, if one orients the links in a canonical way, then these two links have opposite orientations.
Read more about this topic: Pretzel Link
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