标题: shim's Constellation Six (Timur Evbatyrov) [打印本页] 作者: grigr 时间: 2011-3-27 13:27:38 标题: shim's Constellation Six (Timur Evbatyrov)
本帖最后由 grigr 于 2012-7-19 22:27 编辑
see Constellation Six Puzzle from my Friend Timur Evbatyrov
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It's a vertex-turning trigonal dipyramid that has 3 complanar axes of rotation.
Each of the 6 faces has a star image on it and with only 3 possible moves the puzzle gets totally scrambled very easily.
This puzzle has some features that make it somewhat hard to classify.
If you consider Constellation Six as a vertex-turning puzzle, then it's a "normal" puzzle - it always has the same shape.
Only some locked (unturnable) cutting lines make you think that there's still something unusual. Yes, there is - if you consider it an edge turning puzzle, you can say that it constantly changes the shape, bandages some layers and unbandages others. Even the axes change their orientation in space, but the overall shape is "invariant". Can we say it shapeshifts or gets bandaged? You decide.
There are some other mentionable things about this puzzle:
1. Because the small face corner angle is not 36°, but 41.41°, the stars could not have rotational symmetry. And with 36° on the face 90°-turns would not be possible.
2. The ray pieces may play 3 different roles (head, arm, leg) and the small triangle pieces - 2 roles (on big egde or small egde).
3. The circle piece in the center could actually be 13-gon, because each 90° vertex turn turns it by 138.59°, and this repeated 13 times makes it turn by 1801.67°, which is only slightly different from 5 full turn-arounds (5x360° = 1800°).