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Awesome program. Love it.
"Sharpen" seems like "join" (j) applied to only some faces.
"Elongate" and "Gyroelongate" seem like applying "loft" (l) and "Lace" (L) to the bottom of pyramids. These differ some in that you can apply them to an equator regardless of what's north and south. Beautiful.
"Augment" seems like "kis" (k) applied to one face.
"Contract", "Diminish", and "shorten" are all inverses of something or other. Not included in anything I've seen before. ("Gyrate" either.)
"Twist" and "Turn" both toggle between a square and two adjacent triangles - but applied to different places. I'll bet that there are other solids that are separated by such a toggle. (But I don't really know.)
Other notation like in: https://en.wikipedia.org/wiki/Conway_polyhedron_notation
Other question: Do you want to add something like "cupola" operation? Like a hexagon would get 3 squares and 4 triangles glued to it. (This was something else new I learned on your site.) Also it seems like if you did "cupola" on a square, you would get two quadrilaterals and two triangles - and if you did six of them aligned properly, you could morph a cube into a dodecahedron.
Add keyboard shortcuts for the different operators and operator options and update the UI to teach users what shortcuts are available.
Thoughts:
TODO: figure out the rest
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