群論與魔方：魔方花式(上)

F
(fru1, frd2, fld1, flu2)(fr0, fd0, fl0, fu0)
B
(bru2, blu1, bld2, brd1)(br0, bu0, bl0, bd0)
R
(fru2, bru1, brd2, frd1)(fr1, ru1, br1, rd1)
L
(flu1, fld2, bld1, blu2)(fl1, ld1, bl1, lu1)
U
(fru0, flu0, blu0, bru0)(fu0, lu0, bu0, ru0)
D
(frd0, brd0, bld0, fld0)(fd0, rd0, bd0, ld0)
FM
(ru1, rd1, ld1, lu1)(r, d, l, u)
RM
(fu1, bu1, bd1, fd1)(f, u, b, d)
UM
(fr1, fl1, bl1, br1)(f, l, b, r)

 定理1： 設某一角塊和某一邊塊在初始狀態時的顏色標示分別為「XYZ」和「VW」，經任意扭動(這裡指表2所示的操作)魔方後，該角塊的顏色標示只有以下三種可能：「XYZ」、「ZXY」和「YZX」，該邊塊的顏色標示則只有以下兩種可能：「VW」和「WV」。

1. 點(Dot)

RMFM−1RM−1FM = (f, u, r)(b, d, l)     (1)

2. 對角線(Diagonal)

(RLFB)3 = (fru0, blu0)(brd0, fld0)(fr0, bl0)(ru0, lu0)(br0, fl0)(rd0, ld0)(fd0, bd0)(fu0, bu0)     (2)

3. 棋盤(Chessboard)

RM2FM2UM−2 = (fu0, bd0)(bu0, fd0)(ru0, ld0)(rd0, lu0)(fr0, bl0)(fl0, br0)     (3)

4. 十字(Cross)

UR2U2FMD2R2D2FM−1U = (fru0, bld0)(flu0, fld0)(blu0, frd0)(bru0, brd0)     (4)

5. 直條紋(Stripe)

 URU2FMU2R−1FBL2UFM−1RL−1B−1D = (fru1, bru2)(flu1, blu2)(brd2, bld1)(frd2, fld1)(fu0, bu0)(lu1)(ru1)(rd0, ld0)(fd1)(bd1)     (5)

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