正六面体自镜像魔方

明华

&nbsp; <BR>&nbsp; <BR>&nbsp;&nbsp;&nbsp;&nbsp; 我们已经知道 Dino Cube（正六面体八轴二阶魔方）是一个自镜像魔方：<BR>&nbsp;&nbsp;<BR>&nbsp;&nbsp;&nbsp;<BR>&nbsp;&nbsp;&nbsp;&nbsp;<BR>&nbsp;&nbsp;&nbsp;&nbsp; 对于 Dino Cube（正六面体八轴二阶魔方），其在镜子中的所有状态都是 pengw 所说的<BR>“合法状态” ！<BR>&nbsp; <BR>&nbsp; <BR>&nbsp;&nbsp;&nbsp;&nbsp; 请大家参考： <A href="http://bbs.mf8-china.com/viewthread.php?tid=3132"><FONT color=blue><STRONG>The Shortest Solver Of Dino Cube</STRONG></FONT></A>&nbsp;&nbsp;<BR>&nbsp; <BR>&nbsp; &nbsp; <BR>&nbsp; <BR>&nbsp;&nbsp;&nbsp;&nbsp; <A href="http://bbs.mf8-china.com/viewthread.php?tid=3132">http://bbs.mf8-china.com/viewthread.php?tid=3132</A><BR>&nbsp;&nbsp;<BR>&nbsp;&nbsp;<BR>&nbsp;&nbsp;<BR>&nbsp;&nbsp;&nbsp;
<P>&nbsp;&nbsp;&nbsp; Dino Cube（正六面体八轴二阶魔方）可以产生自镜像魔方（这是其它 正六面体魔方 <BR>所 不 具备的）。</P>
<P>&nbsp;&nbsp;&nbsp; 如 原始魔方 <IMG alt="" src="http://bbs.mf8-china.com/data/attachment/forum/dvbbs/2006-12/20061259103269040.gif" border=0>&nbsp;到 她的 自镜像魔方 <IMG alt="" src="http://bbs.mf8-china.com/data/attachment/forum/dvbbs/2006-12/20061259253177267.gif" border=0> 的最少步公式：</P>
<P>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; Generate in many ways&nbsp;&nbsp; <BR><IMG src="http://bbs.mf8-china.com/data/attachment/forum/dvbbs/2006-12/20061258392416731.gif" border=0><BR>&nbsp;&nbsp;&nbsp;&nbsp;<BR>&nbsp;1)&nbsp; 0 1' 7 4' 2' 5 4' 6 5 4 <BR>&nbsp;2)&nbsp; 0 3' 2 4' 5' 7 4' 1 7 4 <BR>&nbsp;3)&nbsp; 0 6' 5 4' 7' 2 4' 3 2 4 <BR>&nbsp;4)&nbsp; 0' 1 2' 4 7 5' 4 3' 5' 4' <BR>&nbsp;5)&nbsp; 0' 3 5' 4 2 7' 4 6' 7' 4' <BR>&nbsp;6)&nbsp; 0' 6 7' 4 5 2' 4 1' 2' 4' <BR>&nbsp;7)&nbsp; 1 0' 3 5' 6' 4 5' 2 4 5 <BR>&nbsp;8)&nbsp; 1 2' 4 5' 3' 6 5' 7 6 5 <BR>&nbsp;9)&nbsp; 1 7' 6 5' 4' 3 5' 0 3 5 <BR>&nbsp;10)&nbsp; 1' 0 6' 5 3 4' 5 7' 4' 5' <BR>&nbsp;11)&nbsp; 1' 2 3' 5 4 6' 5 0' 6' 5' <BR>&nbsp;12)&nbsp; 1' 7 4' 5 6 3' 5 2' 3' 5' <BR>&nbsp;13)&nbsp; 2 1' 0 6' 7' 5 6' 3 5 6 <BR>&nbsp;14)&nbsp; 2 3' 5 6' 0' 7 6' 4 7 6 <BR>&nbsp;15)&nbsp; 2 4' 7 6' 5' 0 6' 1 0 6 <BR>&nbsp;16)&nbsp; 2' 1 7' 6 0 5' 6 4' 5' 6' <BR>&nbsp;17)&nbsp; 2' 3 0' 6 5 7' 6 1' 7' 6' <BR>&nbsp;18)&nbsp; 2' 4 5' 6 7 0' 6 3' 0' 6' <BR>&nbsp;19)&nbsp; 3 0' 6 7' 1' 4 7' 5 4 7 <BR>&nbsp;20)&nbsp; 3 2' 1 7' 4' 6 7' 0 6 7 <BR>&nbsp;21)&nbsp; 3 5' 4 7' 6' 1 7' 2 1 7 <BR>&nbsp;22)&nbsp; 3' 0 1' 7 6 4' 7 2' 4' 7' <BR>&nbsp;23)&nbsp; 3' 2 4' 7 1 6' 7 5' 6' 7' <BR>&nbsp;24)&nbsp; 3' 5 6' 7 4 1' 7 0' 1' 7' <BR>&nbsp;25)&nbsp; 4 2' 3 0' 1' 6 0' 5 6 0 <BR>&nbsp;26)&nbsp; 4 5' 6 0' 3' 1 0' 7 1 0 <BR>&nbsp;27)&nbsp; 4 7' 1 0' 6' 3 0' 2 3 0 <BR>&nbsp;28)&nbsp; 4' 2 1' 0 3 6' 0 7' 6' 0' <BR>&nbsp;29)&nbsp; 4' 5 3' 0 6 1' 0 2' 1' 0' <BR>&nbsp;30)&nbsp; 4' 7 6' 0 1 3' 0 5' 3' 0' <BR>&nbsp;31)&nbsp; 5 3' 0 1' 2' 7 1' 6 7 1 <BR>&nbsp;32)&nbsp; 5 4' 2 1' 7' 0 1' 3 0 1 <BR>&nbsp;33)&nbsp; 5 6' 7 1' 0' 2 1' 4 2 1 <BR>&nbsp;34)&nbsp; 5' 3 2' 1 0 7' 1 4' 7' 1' <BR>&nbsp;35)&nbsp; 5' 4 7' 1 2 0' 1 6' 0' 1' <BR>&nbsp;36)&nbsp; 5' 6 0' 1 7 2' 1 3' 2' 1' <BR>&nbsp;37)&nbsp; 6 0' 1 2' 3' 4 2' 7 4 2 <BR>&nbsp;38)&nbsp; 6 5' 3 2' 4' 1 2' 0 1 2 <BR>&nbsp;39)&nbsp; 6 7' 4 2' 1' 3 2' 5 3 2 <BR>&nbsp;40)&nbsp; 6' 0 3' 2 1 4' 2 5' 4' 2' <BR>&nbsp;41)&nbsp; 6' 5 4' 2 3 1' 2 7' 1' 2' <BR>&nbsp;42)&nbsp; 6' 7 1' 2 4 3' 2 0' 3' 2' <BR>&nbsp;43)&nbsp; 7 1' 2 3' 0' 5 3' 4 5 3 <BR>&nbsp;44)&nbsp; 7 4' 5 3' 2' 0 3' 6 0 3 <BR>&nbsp;45)&nbsp; 7 6' 0 3' 5' 2 3' 1 2 3 <BR>&nbsp;46)&nbsp; 7' 1 0' 3 2 5' 3 6' 5' 3' <BR>&nbsp;47)&nbsp; 7' 4 2' 3 5 0' 3 1' 0' 3' <BR>&nbsp;48)&nbsp; 7' 6 5' 3 0 2' 3 4' 2' 3' <BR>&nbsp; </P><BR>&nbsp;&nbsp;&nbsp;<BR>

乌木

<P>同一“棱块子魔方”的任意态也有自己的镜像，比如下面左图的初态和右图的终态互为镜像：</P>
<P>&nbsp;</P>
<applet code="RubikPlayer.class" codebase=3 width="250" height="250">
<param name="ColorTable" value="0xf8f8f8,0x00732f,0xff4400,0xffd200,0x003373,0x8c000f,0x858585">
  <param name="scrptLanguage" value="SupersetENG">
  <param name="beta" value="29">
  <param name="stickersFront" value="6,5,6,1,6,4,6,4,6">
  <param name="stickersRight" value="6,5,6,2,6,2,6,1,6">
  <param name="stickersDown" value="6,0,6,0,6,0,6,2,6">
  <param name="stickersBack" value="6,0,6,3,6,1,6,1,6">
  <param name="stickersLeft" value="6,3,6,5,6,3,6,2,6">
  <param name="stickersUp" value="6,5,6,4,6,3,6,4,6">
</applet>      <applet code="RubikPlayer.class" codebase=3 width="250" height="250">
<param name="ColorTable" value="0xf8f8f8,0x00732f,0xff4400,0xffd200,0x003373,0x8c000f,0x858585">
  <param name="scrptLanguage" value="SupersetENG">
  <param name="scrpt" value="MR2 MD2 MF2 CR2 ">
  <param name="beta" value="-29">
  <param name="stickersFront" value="6,5,6,1,6,4,6,4,6">
  <param name="stickersRight" value="6,5,6,2,6,2,6,1,6">
  <param name="stickersDown" value="6,0,6,0,6,0,6,2,6">
  <param name="stickersBack" value="6,0,6,3,6,1,6,1,6">
  <param name="stickersLeft" value="6,3,6,5,6,3,6,2,6">
  <param name="stickersUp" value="6,5,6,4,6,3,6,4,6">
</applet>

乌木

至于14楼的心块簇自对称情况相当于同色的四个心块是整体一块，两个魔方态的心块簇对称程度够漂亮的了。

乌木

<P>回复16楼：</P>
<P>&nbsp;</P>
<P>原来这样，四块四块地作中心对称式调动。我再对全色四阶试试，结果如下。心块簇的位置确实成自镜像了。另三面也没问题，图略。如果两个魔方态的任一个，各心块能够再各自就地转合适的90°的话，则对称得更完美了。</P>
<P>&nbsp;</P>
<P> </P>
<P>&nbsp;</P>

[ 本帖最后由 乌木 于 2008-3-21 11:17 编辑 ]

明华

<IMG src="http://bbs.mf8-china.com/attachments/month_0803/20080320_3f0d06c2ff99b2dc90d91VBlSnowNfV2.gif" border=0><BR><BR><BR>&nbsp;&nbsp;&nbsp; 利用楼上的公式也可以 互换 6、7 和 互换 10、11 的位置：<BR><BR><APPLET codeBase=http://bbs.mf100.org height=300 archive=revengeplayer.jar width=300 code=RevengePlayer.class><PARAM NAME="scrgpt" VALUE="CU\n MB' ML' MU' ML U ML' MU ML U' MB\n CU'\n MB' ML' MU' ML U ML' MU ML U' MB\n"><PARAM NAME="stickersup" VALUE="5,5,5,5,5,4,0,5,5,3,1,5,5,5,5,5"><PARAM NAME="scrgptlanguage" VALUE="SupersetENG"><PARAM NAME="colortable" VALUE="0xf8f8f8,0x00732f,0xff4400,0xffd200,0x003373,0x8c000f,0x858585"></APPLET><BR><BR>&nbsp;&nbsp;&nbsp;

[ 本帖最后由 明华 于 2008-3-20 16:28 编辑 ]

明华

&nbsp; <BR>&nbsp; <BR>&nbsp;&nbsp;&nbsp; “心角块”是 pengw 大师发明的叫法，这个您得同他讲！<BR>&nbsp; <BR>&nbsp; <BR>&nbsp;&nbsp;&nbsp; 在“正六面体四阶自镜像魔方”（全色四阶）中很简单，直接用 12 楼的公式嘛！ <BR>这样用：<BR>&nbsp; <BR>&nbsp; <BR><BR>&nbsp;&nbsp;&nbsp; 内对角块镜像公式：（注意：蓝-绿、黄-白）<BR><BR><APPLET codeBase=http://bbs.mf100.org height=300 archive=revengeplayer.jar width=300 code=RevengePlayer.class><PARAM NAME="stickersdown" VALUE="2,2,2,2,2,2,1,2,2,2,0,2,2,2,2,2"><PARAM NAME="scrgpt" VALUE="MR2\n MB' ML' MU' ML U ML' MU ML U' MB\n CU'\n MB' ML' MU' ML U ML' MU ML U' MB\n CU\nMR2\n"><PARAM NAME="stickersup" VALUE="5,5,5,5,5,4,5,5,5,3,5,5,5,5,5,5"><PARAM NAME="scrgptlanguage" VALUE="SupersetENG"><PARAM NAME="colortable" VALUE="0xf8f8f8,0x00732f,0xff4400,0xffd200,0x003373,0x8c000f,0x858585"></APPLET><BR><BR>&nbsp;&nbsp;&nbsp;

[ 本帖最后由 明华 于 2008-3-20 16:28 编辑 ]

乌木

“心角块”是否改叫“偏心块”更合理？

乌木

<P>在纯色四阶中，四个心块看不出区别。在全色四阶中，从颜色来说，下图两个魔方的心块对称，但考虑号码，就不对称。只要下图中任一个魔方的所有同色的6、7互换，所有同色的10、11也互换，则两个魔方的心块就对称了。我不会互换6、7和互换10、11；如果不可能，则全色四阶的心块簇没有自镜像。</P>
<P>&nbsp;</P>
<P> </P>

明华

&nbsp;&nbsp;&nbsp;&nbsp; <BR>&nbsp; <BR>&nbsp;&nbsp;&nbsp; 注：这里“内对角块镜像公式”仅提供 两组角位置互换镜像公式。<BR>&nbsp; <BR>&nbsp; <BR>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<BR>&nbsp;&nbsp;&nbsp; 注：<FONT color=blue><STRONG>中层 特指除去各面“中心块”的其他 中层块 ； 内对角块 也有人称之为 心角块</STRONG></FONT> 。<BR>&nbsp;&nbsp;<BR>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<BR>

[ 本帖最后由 明华 于 2008-3-20 13:15 编辑 ]

明华

<BR><BR>&nbsp;&nbsp;&nbsp; 内对角块镜像公式：（注意：蓝-绿、黄-白）<BR><BR><APPLET height=300 archive=professorplayer.jar  codeBase=http://bbs.mf100.org width=300 code=de.pirzer.rubik.ProfessorPlayerApp.class><PARAM NAME="ColorTable" VALUE="0xf8f8f8,0x00732f,0xff4400,0xffd200,0x003373,0x8c000f,0x858585"><PARAM NAME="scrgptLanguage" VALUE="PirzerENG"><PARAM NAME="scrgpt" VALUE="MRR2\n MBB' MLL' MUU' MLL U MLL' MUU MLL U' MBB\n CU'\nMBB' MLL' MUU' MLL U MLL' MUU MLL U' MBB\n CU\nMRR2\n "><PARAM NAME="stickersDown" VALUE="2,2,2,2,2,2,2,2,1,2,2,2,2,2,2,2,2,2,0,2,2,2,2,2,2"><PARAM NAME="stickersUp" VALUE="5,5,5,5,5,5,4,5,5,5,5,5,5,5,5,5,3,5,5,5,5,5,5,5,5"><PARAM NAME="height" VALUE="300"><PARAM NAME="archive" VALUE="professorplayer.jar"><PARAM NAME="width" VALUE="300"><PARAM NAME="code" VALUE="de.pirzer.rubik.ProfessorPlayerApp.class"><PARAM NAME="codeBase" VALUE="http://bbs.mf8-china.com/"></APPLET><BR><BR>&nbsp;&nbsp;&nbsp;

[ 本帖最后由 明华 于 2008-3-20 13:05 编辑 ]