This is an instantiation of an example on page 52 of Allen Hatcher’s Algebraic Topology. (You can download this book for free.) Here’s how to construct it: Start with the Cartesian product Y × I. Now rotate one end by 1/3 and glue it to the other end. The resulting object has only one boundary and is not a manifold. Now glue a disk along the boundary… I also made a version of just the core (no disk), pictured in the last photo.

This yarn is something knitandperl gave me or swapped me to try.
Goal: shrink the boundary to mimic gluing on a disc.

Used 16” sz 6, 30” sz 6, and 16” sz 2.5 for casting on.
Replaced the sz 2.5 with a 30” sz 6 on round 1.

Cast on 70 st/needle.

Dang. This yarn felts like a smelt.