Algorithms similar to the <R, U, D> E-perm

Discussion in 'General Speedcubing Discussion' started by macky, Sep 11, 2010.

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  1. macky

    macky Premium Member

    Apr 4, 2006
    Stanford, CA
    P = RU'R'DRUR'D'
    Q = DRUR'D'RU'R'
    P' = DRU'R'D'RUR'
    Q' = RUR'DRU'R'D'
    Note that the effects of P and Q are mirrors, as are those of P' and Q'.

    The E-perm popularized by Rowe can then be written x'PQ'x. I wrote a bit of php to generate VisualCube images for all cases of the form
    x'[P/Q/P'/Q'][/F/F'/F2][P/Q/P'/Q']x here. The color scheme can be set here.

    Here are some non-Sune COLL algorithms from this list:
    x'PQx cancelled = x'RU'R'DRU2R'D'RU'R'x

    mirror: x'QPx cancelled = x'DRUR'D'RU2R'DRUR'D'x

    x'P'Q'x cancelled = x'DRU'R'D'RU2R'DRU'R'D'x

    mirror: x'Q'P'x cancelled = x'RUR'DRU2R'D'RUR'x

    x'PFPx = x'RU'R'DRUR'D'FRU'R'DRUR'D'x
    (x'QF'Qx, x'P'F'P'x, x'Q'FQ'x, x'P'F2Px, x'Q'F2Qx all solve the same case.)

    x'P'FQx = x'DRU'R'D'RUR'FDRUR'D'RU'R'x
    mirror: x'Q'F'Px

    x'PF2P'x = x'RU'R'DRUR'D'F2DRU'R'D'RUR'x
    mirror: x'QF2xQ'

    x'P'FPx = x'DRU'R'D'RUR'FRU'R'DRUR'D'x
    mirror: x'Q'F'Qx

    x'PF2Px = x'RUR'DRU'R'D'F2RU'R'DRUR'D'x
    mirror: x'QF2Qx

    x'Q'FQx = x'RUR'DRU'R'D'FDRUR'D'RU'R'x
    mirror: x'P'F'Px
    There may be others that are interesting as ZBLL algorithms.

    The first and the third (inverse) can be conjugated to give these A-perms:
    x'RPQR'x cancelled = x'R2U'R'DRU2R'D'RU'R2x
    x'RQ'P'R'x cancelled = x'R2UR'DRU2R'D'RUR2'x
    These can be used as additional main A-perms to avoid y2.

    If you're interested, here's the php code:

    // base algorithms
    $P = "RU'R'DRUR'D'";
    $Pi = "DRU'R'D'RUR'";
    $Q = "DRUR'D'RU'R'";
    $Qi = "RUR'DRU'R'D'";

    // arrays
    $basearray = array($P, $Pi, $Q, $Qi);
    $insertarray = array("", "F", "F'", "F2");

    <title>Algorithms similar to the <R, U, D> E-perm</title>

    foreach($basearray as $base)
    foreach($insertarray as $insert)
    foreach($basearray as $base2) {
    $case = "x'" . $base . $insert . $base2 . "x";
    echo "<img src=\"/scripts/vcube/visualcube.php?fmt=png&view=plan&case=$case\">";

    It wouldn't be hard to add some formatting or to have the algorithms/shorthands written out.
    Last edited: Sep 11, 2010
  2. qqwref

    qqwref Member

    Dec 18, 2007
    a <script> tag near you
    Clever idea. I really like the use of PHP to generate algs in the form of strings, ignoring cube considerations. Of course, only some of these algs are useful, and using an x' for COLL/OLL isn't generally the best idea because it could get in the way of PLL recognition.
  3. riffz

    riffz Member

    Oct 3, 2008
    Toronto (Canada)
    Just tried the first one. Nice for BLD. I'll check out the rest later.

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