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Does the STOP-cube have a second type of solution?

You might ask: "What the heck is a STOP-cube?" and "Why would I care? Who are you anyways?"
And those are all legit questions of course.

My name is Ortwin, I am a long time member of the twisty puzzle forum. Currently I am looking for the answer to question regarding a specific sticker modification of a 3x3x3 cube, but there did not seem to be much interest over there in the question. Walter Randelshofer who is also a member of this forum recommended to post it into this community, and hereby I do.

To get an idea what that "STOP-cube" is, you might want to have a quick look at the links to the topics in the twistypuzzle forum: