Face-Turning Octahedron (FTO) Tutorial: Bencisco Method

正八面体魔方 (FTO) 教程：Bencisco 解法

The Bencisco Method is the premier speedsolving method for the Face-Turning Octahedron (FTO). This comprehensive guide walks you through the method step by step — from basic notation all the way to solving the last layer. It is designed for people who want to learn to solve the FTO but haven't been able to yet.

Bencisco 解法是正八面体魔方 (Face-Turning Octahedron, 简称 FTO) 的主流速解法。 本教程将手把手带你从基础转动符号开始，一步步学会完整的 FTO 复原方法。 本教程面向想学习 FTO 但还不会复原的玩家。

Note: This tutorial uses the DianSheng color scheme for all explanations.

注意：本教程采用 DianSheng（点盛）配色方案进行说明。

The FTO has 8 faces, each of which can be turned. The standard notation assigns a letter to each face: U (Up), D (Down), L (Left), R (Right), F (Front), B (Back), BL (Back-Left), BR (Back-Right). A prime symbol (') after a letter means counter-clockwise.

FTO 有 8 个面，每个面都可以转动。标准转动符号为每个面分配一个字母： U（上）、D（下）、L（左）、R（右）、 F（前）、B（后）、BL（后左）、BR（后右）。 字母后加撇号(')表示逆时针转动。

For reference, here is the notation used by Twizzle Editor, a very useful interactive tool:

以下是 Twizzle Editor（一个非常实用的在线互动工具）所使用的符号对照表：

Method Overview — 10 Steps:

解法流程 — 共 10 步：

1. 1st Center — Solve the white center face
2. 第一个中心面 (1st Center) — 复原白色中心面
3. F2T (First 2 Triples) — Build 2 white-corner triples
4. F2T（前两个三元组） — 构建 2 个白色角块三元组
5. 2nd Center — Solve the green center face
6. 第二个中心面 (2nd Center) — 复原绿色中心面
7. L2C (Last 2 Centers) — Solve orange & gray centers
8. L2C（最后两个中心面） — 复原橙色和灰色中心面
9. LBT (Last Bottom Triple) — Solve the remaining white triple
10. LBT（最后底层三元组） — 复原剩余的白色三元组
11. L3T (Last 3 Triples) — Solve the last 3 yellow triples (final step)
12. L3T（最后三个三元组） — 复原最后 3 个黄色三元组（最终步骤）

Piece Types

零件类型

The FTO is made of 3 types of pieces: triangles (center triangular facets), edges, and corners. An important distinction from the 3×3: all three piece types move — there is no fixed center piece. Therefore, you must memorize the color scheme in advance.

FTO 由 3 种零件组成：三角块（中心三角面）、棱块和角块。 与三阶魔方的重要区别：所有三种零件都会移动——没有固定的中心块。因此，你需要提前记住配色方案。

DianSheng Color Scheme

DianSheng 配色方案

The DianSheng color scheme uses 8 colors: White, Green, Gray, Orange and Yellow, Red, Blue, Purple.

DianSheng 配色方案使用 8 种颜色： 白、 绿、 灰、 橙 和 黄、 红、 蓝、 紫。

Key adjacency rules to memorize:

需要记住的相邻颜色规则：

• White is surrounded (counter-clockwise) by Red → Blue → Purple
• 白色周围（逆时针）为红 → 蓝 → 紫
• White is opposite Yellow
• 白色对面是 黄色
• Between Red & Blue → Gray
• 红与蓝之间 → 灰色
• Between Blue & Purple → Orange
• 蓝与紫之间 → 橙色
• Between Purple & Red → Green
• 紫与红之间 → 绿色

The Orbit Concept

Orbit（轨道）概念

Although the FTO has 8 faces, not all 8 colors can mix with each other. The colors are divided into two orbits of 4 colors each:

虽然 FTO 有 8 个面，但并非所有 8 种颜色都能相互混合。颜色分为两个轨道 (orbit)，每个轨道包含 4 种颜色：

• Orbit 1: White, Green, Gray, Orange (faces U, F, BL, BR)
• 轨道 1：白、绿、灰、橙（面 U、F、BL、BR）
• Orbit 2: Yellow, Red, Blue, Purple (faces L, R, D, B)
• 轨道 2：黄、红、蓝、紫（面 L、R、D、B）

Because of this property, edges never flip, and corners have only 2 possible orientations (good or flipped) rather than the 4 you might expect. When searching for a piece, you only need to look at the 4 faces in the relevant orbit.

由于这个特性，棱块永远不会翻转，角块也只有 2 种可能的朝向（正确或翻转），而不是你可能预期的 4 种。 寻找零件时，只需查看相关轨道的 4 个面即可。

Basic Hold (1st Center through L2C)

基本持握方式（从第一中心到 L2C）

Hold the FTO with the 1st center face (white) pointing left. This is the default hold for most of the solve. U / U' are executed with triggers (index/middle finger), and R / R' are turned by gripping with the right hand.

将 FTO 的第一个中心面（白色面）朝左持握。这是大部分复原过程的默认持握方式。 U / U' 用手指触发（食指/中指），R / R' 用右手抓握转动。

Sledgehammer & Hedgeslammer

Sledgehammer（雪橇锤）与 Hedgeslammer（篱笆锤）

These two move sequences are used extensively in the LBT and L3T steps. They flip triples.

这两个转动序列在 LBT 和 L3T 步骤中大量使用。它们的作用是翻转三元组。

Goal: Solve the white center face.

目标：复原白色中心面。

A center is generally divided into two shapes: the large trapezoid (a triangle flanked by 2 edges) and the small trapezoid (an edge flanked by 2 triangles). It is recommended to build the large trapezoid first to avoid color-scheme mistakes, especially while you're still learning.

中心面通常分为两个形状：大梯形（1 个三角块夹在 2 个棱块之间）和小梯形（1 个棱块夹在 2 个三角块之间）。 建议先构建大梯形，以避免配色错误，尤其是在初学阶段。

Remember: in the DianSheng color scheme, white is surrounded counter-clockwise by Red → Blue → Purple. The Red-Blue relationship is the same as on a 3×3, which can help as a reference point.

记住：在 DianSheng 配色中，白色周围逆时针为红 → 蓝 → 紫。红蓝关系与三阶魔方相同，可以作为参考。

Here are 3 useful small-trapezoid algorithms (these create a small trapezoid on the U face, minimizing rotations):

以下是 3 个实用的小梯形公式（在 U 面形成小梯形，减少持换）：

When the two triangles are far apart:

当两个三角块距离较远时：

When the two triangles are close together:

当两个三角块距离较近时：

When both triangles are on the same face:

当两个三角块在同一面上时：

Goal: Build 2 triples around white corners (leave one spot open, like Yau cross edges).

目标：围绕白色角块构建 2 个三元组（留一个空位，类似 Yau 方法的十字棱块）。

Hold the FTO in the basic hold (white face left). Use only moves that don't break the white center: U / U', R / R', r / r', and Rv / Rv' rotations.

以基本持握方式（白色面朝左）持握 FTO。只使用不破坏白色中心的转动： U / U'、R / R'、r / r' 和 Rv / Rv' 持换。

This step has very high degrees of freedom, so it may feel difficult at first. Keep practicing — repeatedly scramble and re-solve to get comfortable with the FTO's unique movement patterns. Watching example solves on YouTube is also very helpful.

这一步自由度非常高，所以一开始可能会觉得困难。坚持练习——反复打乱和复原，熟悉 FTO 独特的运动模式。观看 YouTube 上的示范解法也非常有帮助。

Goal: Solve the green center face.

目标：复原绿色中心面。

It's best to fix the color of the 2nd center you solve. This tutorial solves the green center. Just like the 1st center, build the large trapezoid first, then the small trapezoid.

最好固定第二个中心面的颜色。本教程选择复原绿色中心。 与第一中心面一样，先构建大梯形，再构建小梯形。

Now that F2T is done, your available moves are more restricted. Only use: U / U', R / R', r / r'.

由于 F2T 已完成，可用转动更加受限。只使用： U / U'、R / R'、r / r'。

Green center color reference: looking at the green face, counter-clockwise → Yellow → Red → Purple. Be careful with the color scheme.

绿色中心配色参考：正视绿色面时，逆时针 → 黄 → 红 → 紫。注意配色。

After completing the 2nd center, do an AUF (Adjust U Face) so that the yellow edge faces right.

完成第二中心面后，进行 AUF（调整 U 面），使黄色棱块朝右。

Goal: Solve the remaining 2 center faces (orange & gray).

目标：复原剩余的 2 个中心面（橙色和灰色）。

While maintaining the basic hold, set the orange face as U (the gray face becomes F). Solving either orange or gray will automatically solve the other one.

保持基本持握方式，将橙色面设为 U 面（灰色面变为 F 面）。 复原橙色或灰色中任一面，另一面也会自动复原。

Again, start by building the large trapezoid. The key moves are:

同样从大梯形开始构建。关键转动为：

Combine these with U / U' between them to solve L2C without breaking the 2nd center.

在这些公式之间穿插 U / U'，即可在不破坏第二中心面的情况下复原 L2C。

After L2C, make sure both orange and gray centers have their yellow edges facing right (AUF both).

L2C 完成后，确保橙色和灰色中心面的黄色棱块都朝右（两面都进行 AUF）。

Goal: Solve the remaining white triple that was left open during F2T.

目标：复原 F2T 时留下的最后一个白色三元组。

From this step onward, switch to holding the yellow face as U. You will now heavily use Sledgehammer and Hedgeslammer.

从这一步开始，切换为黄色面朝上的持握方式。 接下来将大量使用雪橇锤和篱笆锤。

How it works: Sledge/Hedge flips the two triples moved by the first turn. By flipping triples and interleaving U / U' moves, you align the white corner with its matching triangles.

原理：雪橇锤/篱笆锤会翻转第一步移动的两个三元组。通过翻转三元组并穿插 U / U' 转动，将白色角块与对应的三角块对齐。

Example solve (LBT):

示范解法（LBT）：

In this example: After a Uv' rotation, the white corner is at the back-right and a red triangle is at the top-left of U. The first inverse Sledgehammer flips the red triangle to the side without flipping the white corner. Then U' aligns red. The second inverse Sledgehammer flips both the corner and the purple triangle. Then U completes the triple.

在此示例中：Uv' 持换后，白色角块在右后方，红色三角块在 U 面左后方。 第一个逆雪橇锤将红色三角块翻到侧面，而不翻转白色角块。然后 U' 对齐红色。 第二个逆雪橇锤同时翻转角块和紫色三角块。然后 U 完成三元组。

Once the triple is built, insert it into the empty slot below. There are 2 insertion patterns depending on whether the white sticker faces up or to the side. Use D / D' to align the slot (then ADF — Adjust D Face — afterward).

三元组构建完成后，将其插入下方的空位。根据白色贴纸朝上或朝侧面，有 2 种插入模式。使用 D / D' 对齐空位（之后进行 ADF — 调整 D 面）。

Goal: Match the yellow corners with the yellow triangles. This is the hardest step of Bencisco.

目标：将黄色角块与黄色三角块匹配。这是 Bencisco 中最难的一步。

Continue holding yellow face as U. Use Sledgehammer, Hedgeslammer, and U / U' moves.

继续以黄色面朝上持握。使用雪橇锤、篱笆锤和 U / U' 转动。

Identifying the Case

判断情况

Look at the U face and check:

观察 U 面并检查：

• How many side-colored (non-yellow) triangles are on the U face?
• U 面上有多少个非黄色三角块？
• Are any corners flipped?
• 是否有角块翻转？
• Where are the side triangles located?
• 侧面三角块的位置在哪？

In all other cases, apply H (R B' R' B) to reach a standard state with all yellow on top but triangles mismatched on the sides.

在所有其他情况下，执行 H（R B' R' B）以达到标准状态——所有黄色朝上，但侧面三角块错位。

Even vs. Odd Parity

偶数 (Even) 与奇数 (Odd) 奇偶性

Once you reach the standard state, classify it as even or odd:

达到标准状态后，将其分类为偶数 (even) 或奇数 (odd)：

Even Case

偶数情况 (Even)

Re-orient the puzzle and observe the relationship between the flipped corner's side color and the adjacent triangle color. There are 3 sub-patterns — apply the matching Sledgehammer or Hedgeslammer to solve the yellow face.

重新调整方向，观察翻转角块侧面颜色与相邻三角块颜色的关系。共有 3 种子模式——执行对应的雪橇锤或篱笆锤来复原黄色面。

After the yellow face is solved, check the corners. If they're correct — congratulations, the FTO is solved! If not, apply one of the CP (Corner Permutation) algorithms:

黄色面复原后，检查角块。如果正确——恭喜，FTO 复原完成！ 如果不正确，执行以下 CP（角块排列）公式之一：

CP1 (clockwise顺时针):

CP2 (counter-clockwise逆时针):

Odd Case

奇数情况 (Odd)

Re-orient the puzzle and check the side color of the flipped corner. There are 3 sub-patterns. Apply the corresponding algorithm to solve the yellow face.

重新调整方向并检查翻转角块的侧面颜色。共有 3 种子模式。 执行对应公式来复原黄色面。

After solving the yellow face in an odd case, the side triangles will always have a 2-swap (two triangles exchanged). Apply the 2-swap algorithm:

在奇数情况下复原黄色面后，侧面三角块一定会出现二元交换（两个三角块互换）。执行二元交换公式：

2-Swap Algorithm:二元交换公式：

(where 2L = br' BR)（其中 2L = br' BR）

If you need more help or want to get faster, check out these resources:

如果需要更多帮助或想提高速度，请参考以下资源：

• FTO Notation (Twizzle Editor)
  Detailed interactive notation reference. 详细的互动转动符号参考。
• Chris Choi's Bencisco Tutorial (YouTube)Chris Choi 的 Bencisco 教程（YouTube）
  If anything in this article is unclear, check this video tutorial. 如果本教程有不清楚的地方，可以参考这个视频教程。
• Benpuzzles' Bencisco Explanation (YouTube Playlist)Benpuzzles 的 Bencisco 讲解（YouTube 播放列表）
  Created by Ben Streeter (the inventor of Bencisco). Step-by-step playlist — consult the specific video for any step you're struggling with. 由 Ben Streeter（Bencisco 发明者）制作。逐步讲解播放列表——遇到困难的步骤时可以查看对应视频。
• FTO Friday (YouTube Playlist)
  EddtheRexMan's series on advanced Bencisco techniques. Regularly updated. EddtheRexMan 的 Bencisco 进阶技巧系列。持续更新中。
• LBT Algorithm TableLBT 公式表
  Complete set of LBT algorithms. You don't need to memorize them all, but browsing through can give you useful insights. 完整的 LBT 公式集。不需要全部记住，但浏览一下会有有用的启发。
• OLP Algorithm Table (by Ben Streeter)OLP 公式表（Ben Streeter 制作）
  Algorithms for solving L3T in a single look. Memorizing these eliminates mid-step decisions and speeds you up. 用于一次观察完成 L3T 的公式集。记住这些公式可以省去中途判断，提高速度。
• TCP Algorithm TableTCP 公式表
  Created by Edd Dibley with Japanese annotations by Kitamura-san. A great starting point for learning TCP algorithms. 由 Edd Dibley 制作，北村先生加注日文。学习 TCP 公式的好起点。
• L3T Algorithm Table (Aedan Bryant)L3T 公式表（Aedan Bryant 制作）
  Comprehensive L3T algorithm collection (some gaps). Recommended for those who want to learn more algorithms. 全面的 L3T 公式集（部分空缺）。推荐给想学习更多公式的玩家。
• L3T Algorithm Table (Nathan)L3T 公式表（Nathan 制作）
  Another comprehensive L3T reference, similar in content to Aedan's table. 另一个全面的 L3T 参考资料，内容与 Aedan 的表格类似。
• Cubing History: Bencisco Method
  Historical records and original documentation. 历史记录和原始文档。
• Ben Streeter's Original Bencisco DocumentBen Streeter 的 Bencisco 原始文档

Hardware Setup & Maintenance Tips

• Lube Choice: Magnetic FTOs benefit from medium-viscosity silicon lube on the core combined with a light lube on piece tracks to prevent lockups.
• Tensions: Keep core tensions even across all 8 faces to ensure uniform corner-cutting angles.
• Discount Code: Use code CUBINGPRO at checkout on TheCubicle or SpeedCubeShop to get 5% OFF your order!