MIT Mystery Hunt 2020/Catenoid

Catenoid is a crossword from the round of the 2020 MIT Mystery Hunt.

Puzzle Elements
Flavortext - ''You can find a 3D schematic for this ride in one of the two display cases containing prototype rides as you climb up CHORD. This ride is Model 40.''

Hint in Flavortext - The flavortext mostly is there to point solvers towards the grid used in the puzzle.

I Have Traveled Forty Parsecs - While the hunt was live, solvers had to access the grid by physically going to the Building 2 stairwell (home to the artwork Chord) and walking up to the second floor, which has a display case housing a number of 3D models, including the subject of the puzzle (Model 40).

Task Completion - Remote solvers could instead submit a sonnet about a catenoid (or a cat, annoyed) in order to obtain pictures of the model.

Something Different - The clues solve to not-necessarily dictionary-nature phrases.

Crossword (Special Grid, Cylindrical) - The crossword clues are to be filled into the grid on the catenoid's surface, which reduces down to a Tetrakis square tiling with 16 columns and 10 rows that wrap around in a cylindrical fashion. As such, entries cross two letters at a time in potentially opposite directions.

Positional Extraction - In a twist on extraction from double letters, this puzzle extracts from a continuous diagonal of cells that form diamond-shapes containing the same letter.