View source for Zeta-Bp8/L8E Algorithms

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📢 '''Notice:''' Please be advised that our algorithm library will undergo a major update in the near future.
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The '''Zeta-Bp8 L8E Algorithm Sheet''' contains the official slice-free algorithm subsets used in the final stage of the [[Zeta-Bp8]] method. Developed and compiled by '''Hiori (Bernardo Pietro)''', these algorithms are strictly optimized for pure outer-layer ergonomics (<tt><U, D, R, L, F, B></tt>), completely avoiding <tt>M, S, and E</tt> slice turns to prevent mechanical lockups during high-speed execution.

All cases listed below have been verified using optimal solvers, yielding highly efficient solutions ranging from 13 to 15 moves.

== Emergency Rule (Non-Recognition) ==
{| class="wikitable" style="background:#fff9e6; border-left: 5px solid #ffcc00; width:100%; padding:10px;"
| '''Panic/Emergency Rule:''' If you encounter an L8E configuration that you do not recognize or have not memorized yet, '''execute the L8E RouxEo algorithm twice'''. This will safely manipulate the edge states into a predictable orientation or a recognizable pattern without disturbing your completed Zeta blocks.
|}

== 1. Orientation & Core Roux-Style Extensions ==
This subset covers base edge orientation states and transitions derived from standard last-edge profiles, adapted for a slice-free finish.

{| class="wikitable" style="width:100%;"
! style="background:#b3c6ff; width:20%;" | Case Name
! style="background:#b3c6ff; width:65%;" | Algorithm
! style="background:#b3c6ff; width:15%;" | Move Count
|-
| '''L8E RouxEo''' || <tt>U' B' F' D2 F2 R F2 L' B2 F2 R U2 B' F' U2</tt> || 15f*
|-
| '''L8E 2-1L UO''' || <tt>U F R U2 R' F' R' F R B L2 B' U2</tt> || 13f*
|-
| '''L8E F-Front''' || <tt>L2 B F' D' B' L D' B' F L U' B L'</tt> || 13f*
|}

== 2. Arrow & Double Arrow Patterns ==
These cases feature specific "Arrow" shapes formed by misoriented edges on the top and bottom layers.

{| class="wikitable" style="width:100%;"
! style="background:#b3c6ff; width:20%;" | Case Name
! style="background:#b3c6ff; width:65%;" | Algorithm
! style="background:#b3c6ff; width:15%;" | Move Count
|-
| '''L8E I-Arrow''' || <tt>B2 F2 D F2 L R U2 L2 B L R' U' B2 R2 U'</tt> || 15f*
|-
| '''L8E ArrowPermutation''' || <tt>B F' L B' F U' F2 L2 F2 U' R2 B2 R2 U'</tt> || 14f*
|-
| '''L8E Double R-Arrow''' || <tt>U' R2 D' L R' U2 F' D2 U2 B D2 B L' R' U</tt> || 15f*
|}

== 3. S and S2 (Sub-Symmetric) Sets ==
A dense algorithmic subset addressing complex sub-symmetric configurations where multiple pieces require simultaneous orientation and swapping.

{| class="wikitable" style="width:100%;"
! style="background:#b3c6ff; width:20%;" | Case Name
! style="background:#b3c6ff; width:65%;" | Algorithm
! style="background:#b3c6ff; width:15%;" | Move Count
|-
| '''L8E S-0''' || <tt>U2 L' R F' L R U' L R' F R2 B L' R U2</tt> || 15f*
|-
| '''L8E S2-A''' || <tt>B2 F2 D' R' U' R' B' F2 D R D F R' B' U</tt> || 15f*
|-
| '''L8E S2-B''' || <tt>L' R' F' U2 L' R' F2 U L2 F2 L2 D U R2</tt> || 14f*
|-
| '''L8E S2-C''' || <tt>R2 B F D2 R' D2 L U2 B' F L2 D' B2 L2 U'</tt> || 15f*
|-
| '''L8E S2-D''' || <tt>F D2 F2 D2 F2 D' B' R B' F D' B L' B</tt> || 14f*
|-
| '''L8E S2-E''' || <tt>F2 L2 F2 U' B2 U B L' B' R2 D' B' L B' U'</tt> || 15f*
|}

== 4. E Sets & Special Unnamed Variants ==
Advanced endgame permutations characterized by intersecting edge pairs across opposite faces.

{| class="wikitable" style="width:100%;"
! style="background:#b3c6ff; width:20%;" | Case Name
! style="background:#b3c6ff; width:65%;" | Algorithm
! style="background:#b3c6ff; width:15%;" | Move Count
|-
| '''L8E E-A''' || <tt>L R D2 R2 F' D2 B' L2 U2 L' R' U' L2 U'</tt> || 14f*
|-
| '''L8E E-B''' || <tt>F' U' F L' R D' R2 D' U F' D2 U' L R'</tt> || 14f*
|-
| '''L8E Special Var. 1''' || <tt>U' F2 L' R' D2 F D2 F' L' R' B2 R2 U' L2 U2</tt> || 15f*
|-
| '''L8E Special Var. 2''' || <tt>B' F D' U F D U' R B' F D B2 F2 U</tt> || 14f*
|}

== Navigation ==
* Return to the main [[Zeta-Bp8]] documentation page.

[[Category:Algorithm sets]]