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Bandaged Brainball
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Brainballs with several pieces glued together. There are 12 meaningful variants. 6 are implemented here.

Like many other puzzles the Brainball can be bandaged by gluing several pieces together. One might ask how many ways are there to do this. In case of the brainball this question can be answered with a analysis made by hand:
There are 2^13=8192 ways to fuse pieces of the Brainball.
There are 136 variants when you neglect symmetries. Of these
52 are derivates of other variants.
26 can't move in any way.
37 have implicit bonds which means they are incomplete.
8 are definitely trivial.
12 remain.

One of the remaing variants is the unbandaged Brainball. Whether the last 12 variants are worth to be reconsidered can't be decided by objective measures as the other classifications above.
The images here show six of the 12 variants which were choosen by the builder as a matter of taste. The number in the captions represent how many pieces are connected to which degree.

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