Rubik’s Cube — 54-sticker demo
Face turns are permutations of 54 facelets. Scramble, then apply the inverse — you return to the identity (solved). Based on the local derivation demo; TheMathFlow video is inspiration only (no on-screen formulas invented here). Not a CFOP solver.
Moves
Face net
Three interlocking rings
Edge 4-cycles from generators U / R / F (video motif is three rings, not six).
How this maps to the math
中文简述：已还原态 = 群单位元。六个面转生成元是 54 贴纸上的置换； 串乘对应复合；逆序列把状态送回单位元。完整中文课见 teach.html；简报见 docs/math.md。本页不发明视频里没有的公式。
- Identity = solved: all 54 stickers on home colors →
solved=true. - Generators:
U D L R F B(and'/2) as length-54 perms. - Scramble then inverse: word \(w\) then \(w^{-1}\) restores \(e\).
- Teaching page (Chinese, 【事实】 / 【视频观察】 / 【假设】 tagged): teach.html.
- Shorter writeup: docs/math.md.
如何运行 demo
本页的 Apply scramble / Apply inverse 与仓库里的
python/demo.py 是同一条路：拧乱再取逆，回到已解（单位元）。
默认拧法 R U R' U'。
在仓库根目录执行（Python 3.10+，仅标准库）：
python3 python/demo.py python3 python/demo.py "F R U R' U' F'"
完整捕获输出：sample-output.txt · 中文课：teach.html · 数学简报：docs/math.md
themathflow.mp4 只作本地参考，不随本仓库上传；片内无文字公式。
3. Scramble: R U R' U' tokens: ['R', 'U', "R'", "U'"] ... solved=False stickers_off_home=12 4. Inverse sequence → expect solved inverse tokens: ['U', 'R', "U'", "R'"] ... solved=True stickers_off_home=0 5. Result scramble then inverse returns to solved: True OK — face turns permute stickers; inverse restores identity.