From dfd2150deb85dc673d4c49715cb6feb4574348c1 Mon Sep 17 00:00:00 2001 From: HactarCE <6060305+HactarCE@users.noreply.github.com> Date: Tue, 8 Jul 2025 18:35:05 -0700 Subject: [PATCH 1/8] Add 7 Hypercubing standards --- README.md | 1 + .../index.md | 133 ++++++++++++++++++ 2 files changed, 134 insertions(+) create mode 100644 draft/7/4d-projection-and-basic-hypercube-twists/index.md diff --git a/README.md b/README.md index 0c12a31..4c4fc1d 100644 --- a/README.md +++ b/README.md @@ -10,6 +10,7 @@ Contribute [on GitHub](https://github.com/cubing/standards). 4. [3x3x3 State Representations](./draft/4/3x3x3-state-representations/) (Draft) 5. [Binary 3x3x3 Encoding](./draft/5/binary-3x3x3-encoding/) (Draft) 6. [SiGN and LGN](./draft/6/sign-lgn-notation/) (Draft) +7. [4D Projection and Basic Hypercube Twists](./draft/7/4d-projection-and-basic-hypercube-twists/) (Draft) ## Future Ideas diff --git a/draft/7/4d-projection-and-basic-hypercube-twists/index.md b/draft/7/4d-projection-and-basic-hypercube-twists/index.md new file mode 100644 index 0000000..d696dc6 --- /dev/null +++ b/draft/7/4d-projection-and-basic-hypercube-twists/index.md @@ -0,0 +1,133 @@ +# Cubing Standard #7: 4D Projection and Basic Hypercube Twists (DRAFT) + +Status: `DRAFT` +Prescriptive or descriptive: descriptive (this standard attempts to describe existing conventions) + +This standard describes the basic moves for a NxNxNxN facet-turning hypercube. + +## 7.1 Polytope elements + +When possible, pieces are named according to the rank of the element of the polytope they correspond to. Let _n_ be the rank of the puzzle. + +| Rank of element | Name | +| --------------- | ------ | +| 0 | Corner | +| 1 | Edge | +| 2 | Face | +| 3 | Cell | +| _n_ - 3 | Peak | +| _n_ - 2 | Ridge | +| _n_ - 1 | Facet | + +These terms are taken from [Polytope - Wikipedia](https://en.m.wikipedia.org/wiki/Polytope#Elements), with the exception of "corner" instead of "vertex." + +The terms "corner" and "edge" are preferred over "peak," "ridge," and "facet." For puzzles in 4 or more dimensions, the terms "peak", "ridge", and "facet" are preferred over "face" and "cell." + +For a 4D hypercube, the terms "corner," "edge," "ridge," and "facet" are preferred, although "cell" is also in common use. + +## 7.1 Facets + +A **facet** is the (N-1)-dimensional element of a polytope. A **cell** is 3-dimensional element. For a 4D polytope, "facet" and "cell" are interchangeable. + +There are 8 facets of a 4-dimensional hypercube: + +| Facet letter | Facet name | Vector | Standard color | +| ------------ | ---------- | ---------- | -------------- | +| `R` | Right | positive X | Red | +| `L` | Left | negative X | Orange | +| `U` | Up | positive Y | White | +| `D` | Down | negative Y | Yellow | +| `F` | Front | positive Z | Front | +| `B` | Back | negative Z | Back | +| `O` | Out | positive W | Pink | +| `I` | In | negative W | Purple | + +Note: historically, `K` ("kata") has been used instead of `I`, and `A` ("ana") or `T` ("top") have been used instead of `I`. It is recommended to avoid these because it is confusing which one corresponds to which cell. Furthermore, `A` conflicts with 5D notation (`A` for "anterior") and `T` has been reappropriated for general F2L notation (`T` for general "top"). + +These also define the standard projection: + +- Positive X pointing to the right +- Positive Y pointing up +- Positive Z pointing forward toward the 3D camera +- Positive W pointing forward toward the 4D camera + +The `O` facet is typically hidden, but the other seven facets are typically visible and spaced apart. The default 3D camera may have a rotational offset applied to give a better view of the 7 facets as follows: + +- `R` may point more forward and down +- `F` may point more left and down +- `U` may point more forward + +## 7.2 Clockwise Twists + +Twists are named using 2, 3, or 4 letters, each corresponding to a facet. All letters are uppercase, with no space or punctuation between them. The first letter indicates which facet is rotated; the remaining letters describe the polytope element that is fixed by the twist. Letters other than the first one may be specified in any order. The twist occurs in a 2D plane, over the minimum nonzero angle necessary to restore the puzzle to its original shape. + +| Twist type | Number of letters | Angle | Example | +| ------------ | ----------------- | ----- | ------- | +| Ridge twist | 2 | 90° | `IR` | +| Edge twist | 3 | 180° | `OUR` | +| Corner twist | 4 | 120° | `DUFR` | + +Rotations appear clockwise when the 4D camera is facing along the vector of the first facet and the 3D camera is facing along the _opposite_ vector from the polytope element described by the second facet. For example, the twist `IR` twists a layer of the `I` facet from positive Z to positive Y, which keeps the vector along the X axis fixed. + +Examples: + +| Twist name | Description | +| ---------- | ------------------------------------------------------------------------ | +| `IR` | `R` twists 90° from `F` to `U` | +| `OUR` | `O` twists 180°, such that `U` and `R` swap and `F` and `B` swap | +| `DUFR` | `D` twists 120° clockwise, such that `F` goes to `I` and `I` goes to `R` | +| | | + +In software with mouse controls, these twists are typically executed by right-clicking on the described sticker. For example, `DUFR` is executed by right-clicking on the `D` sticker of the `DUFR` corner piece. + +## 7.3 Double Twists + +Ridge twists may be doubled by appending `2` to the move. For example, `DF2` denotes the `DF` twist repeated twice. + +Edge twists have order 3 and so do not need to be doubled. + +Corner twists have order 2 and so do not need to be doubled. + +## 7.4 Counterclockwise Twists + +Twists may be suffixed with `'` to invert them. Alternatively, all but the first letter may be replaced with the letter of the opposite facet. For example, the inverse of `IUR` is `IUR'` or `IDL`. + +## 7.5 Layers + +Twists may be prefixed with a layer or layer range using SiGN Notation. + +## 7.5 Slice Twists + +There are four middle slice layers. Slice twists are constructed from facet twists on a parallel facet according to the following table. + +| Letter | Mnemonic | Parallel facet | +| ------ | ------------ | -------------- | +| `M` | "Middle" | `L` | +| `E` | "Equitorial" | `D` | +| `S` | "Standing" | `F` | +| `P` | "Planetary" | `O` | + +For example, `MD` is equivalent to `2LD` + +## 7.6 xyz Notation + +Ridge twists may instead be specified using a facet letter followed by a lowercase letter `x`, `y`, or `z`. Each combination of a facet and lowercase `x`/`y`/`z` maps to a ridge turn based on its projection in 3D. In the following table, `_` represents the facet letter. + +| Facet | `_x` | `_y` | `_z` | +| ----- | ---- | ---- | ---- | +| `R` | `RO` | `RU` | `RF` | +| `L` | `LI` | `LU` | `LF` | +| `U` | `UR` | `UO` | `UF` | +| `D` | `DR` | `DI` | `DF` | +| `F` | `FR` | `FU` | `FO` | +| `B` | `BR` | `BU` | `BI` | +| `O` | `OL` | `OD` | `OB` | +| `I` | `IR` | `IU` | `IF` | + +For example, `Fz` is equivalent to `FO`. + +This notation is generally preferred for puzzle keybinds, for Melinda's 2x2x2x2, and for other physical puzzles. It should be avoided otherwise. + +## 7.6.1 Legacy xyz Notation + +Edge and corner twists may be represented using two `x`/`y`/`z` letters, where the last one may be followed by the digit `2` (which applies only to the last letter), but this is discouraged. It is preferred to group multiple ridge twists using parentheses. For example, `Ozx2` should instead be represented as `(Oz Ox2)` or simply `OUFR`. From 630bff1725e12da7f97e83317790dc50583b8130 Mon Sep 17 00:00:00 2001 From: HactarCE <6060305+HactarCE@users.noreply.github.com> Date: Fri, 11 Jul 2025 18:29:22 -0400 Subject: [PATCH 2/8] =?UTF-8?q?Use=20`=C3=97`=20instead=20of=20`x`?= MIME-Version: 1.0 Content-Type: text/plain; charset=UTF-8 Content-Transfer-Encoding: 8bit --- draft/7/4d-projection-and-basic-hypercube-twists/index.md | 4 ++-- 1 file changed, 2 insertions(+), 2 deletions(-) diff --git a/draft/7/4d-projection-and-basic-hypercube-twists/index.md b/draft/7/4d-projection-and-basic-hypercube-twists/index.md index d696dc6..577edf2 100644 --- a/draft/7/4d-projection-and-basic-hypercube-twists/index.md +++ b/draft/7/4d-projection-and-basic-hypercube-twists/index.md @@ -3,7 +3,7 @@ Status: `DRAFT` Prescriptive or descriptive: descriptive (this standard attempts to describe existing conventions) -This standard describes the basic moves for a NxNxNxN facet-turning hypercube. +This standard describes the basic moves for a N×N×N×N facet-turning hypercube. ## 7.1 Polytope elements @@ -126,7 +126,7 @@ Ridge twists may instead be specified using a facet letter followed by a lowerca For example, `Fz` is equivalent to `FO`. -This notation is generally preferred for puzzle keybinds, for Melinda's 2x2x2x2, and for other physical puzzles. It should be avoided otherwise. +This notation is generally preferred for puzzle keybinds, for Melinda's 2×2×2×2, and for other physical puzzles. It should be avoided otherwise. ## 7.6.1 Legacy xyz Notation From 5b2ea926ef9a54f9144e6f22e22595913b8fbb4c Mon Sep 17 00:00:00 2001 From: HactarCE <6060305+HactarCE@users.noreply.github.com> Date: Fri, 11 Jul 2025 21:54:10 -0400 Subject: [PATCH 3/8] Clarify standard colors --- .../index.md | 26 +++++++++---------- 1 file changed, 12 insertions(+), 14 deletions(-) diff --git a/draft/7/4d-projection-and-basic-hypercube-twists/index.md b/draft/7/4d-projection-and-basic-hypercube-twists/index.md index 577edf2..c247d0b 100644 --- a/draft/7/4d-projection-and-basic-hypercube-twists/index.md +++ b/draft/7/4d-projection-and-basic-hypercube-twists/index.md @@ -27,20 +27,18 @@ For a 4D hypercube, the terms "corner," "edge," "ridge," and "facet" are preferr ## 7.1 Facets -A **facet** is the (N-1)-dimensional element of a polytope. A **cell** is 3-dimensional element. For a 4D polytope, "facet" and "cell" are interchangeable. - -There are 8 facets of a 4-dimensional hypercube: - -| Facet letter | Facet name | Vector | Standard color | -| ------------ | ---------- | ---------- | -------------- | -| `R` | Right | positive X | Red | -| `L` | Left | negative X | Orange | -| `U` | Up | positive Y | White | -| `D` | Down | negative Y | Yellow | -| `F` | Front | positive Z | Front | -| `B` | Back | negative Z | Back | -| `O` | Out | positive W | Pink | -| `I` | In | negative W | Purple | +There are 8 facets of a 4-dimensional hypercube, along with the color in standard orientation: + +| Facet letter | Facet name | Vector | Color | +| ------------ | ---------- | ---------- | ------ | +| `R` | Right | positive X | Red | +| `L` | Left | negative X | Orange | +| `U` | Up | positive Y | White | +| `D` | Down | negative Y | Yellow | +| `F` | Front | positive Z | Front | +| `B` | Back | negative Z | Back | +| `O` | Out | positive W | Pink | +| `I` | In | negative W | Purple | Note: historically, `K` ("kata") has been used instead of `I`, and `A` ("ana") or `T` ("top") have been used instead of `I`. It is recommended to avoid these because it is confusing which one corresponds to which cell. Furthermore, `A` conflicts with 5D notation (`A` for "anterior") and `T` has been reappropriated for general F2L notation (`T` for general "top"). From 392eece665649de80dd383c4c7c0b1311d819f6d Mon Sep 17 00:00:00 2001 From: HactarCE <6060305+HactarCE@users.noreply.github.com> Date: Fri, 11 Jul 2025 21:54:49 -0400 Subject: [PATCH 4/8] Clarify dimension variable --- .../4d-projection-and-basic-hypercube-twists/index.md | 10 +++++----- 1 file changed, 5 insertions(+), 5 deletions(-) diff --git a/draft/7/4d-projection-and-basic-hypercube-twists/index.md b/draft/7/4d-projection-and-basic-hypercube-twists/index.md index c247d0b..59d600d 100644 --- a/draft/7/4d-projection-and-basic-hypercube-twists/index.md +++ b/draft/7/4d-projection-and-basic-hypercube-twists/index.md @@ -7,7 +7,7 @@ This standard describes the basic moves for a N×N×N×N facet-turning hypercube ## 7.1 Polytope elements -When possible, pieces are named according to the rank of the element of the polytope they correspond to. Let _n_ be the rank of the puzzle. +When possible, pieces are named according to the rank of the element of the polytope they correspond to. Let _d_ be the rank (i.e., dimension) of the puzzle. | Rank of element | Name | | --------------- | ------ | @@ -15,15 +15,15 @@ When possible, pieces are named according to the rank of the element of the poly | 1 | Edge | | 2 | Face | | 3 | Cell | -| _n_ - 3 | Peak | -| _n_ - 2 | Ridge | -| _n_ - 1 | Facet | +| _d_ - 3 | Peak | +| _d_ - 2 | Ridge | +| _d_ - 1 | Facet | These terms are taken from [Polytope - Wikipedia](https://en.m.wikipedia.org/wiki/Polytope#Elements), with the exception of "corner" instead of "vertex." The terms "corner" and "edge" are preferred over "peak," "ridge," and "facet." For puzzles in 4 or more dimensions, the terms "peak", "ridge", and "facet" are preferred over "face" and "cell." -For a 4D hypercube, the terms "corner," "edge," "ridge," and "facet" are preferred, although "cell" is also in common use. +For a 4D hypercube, the terms "corner," "edge," "ridge," and "facet" are preferred, although "cell" is also in common use. In 4D specifically, "facet" and "cell" are interchangeable. ## 7.1 Facets From 0fbf92363be45db3e5b28ab306a250229221464b Mon Sep 17 00:00:00 2001 From: HactarCE <6060305+HactarCE@users.noreply.github.com> Date: Fri, 11 Jul 2025 21:55:05 -0400 Subject: [PATCH 5/8] Remove note about `T` ambiguity --- draft/7/4d-projection-and-basic-hypercube-twists/index.md | 2 +- 1 file changed, 1 insertion(+), 1 deletion(-) diff --git a/draft/7/4d-projection-and-basic-hypercube-twists/index.md b/draft/7/4d-projection-and-basic-hypercube-twists/index.md index 59d600d..fa69cd6 100644 --- a/draft/7/4d-projection-and-basic-hypercube-twists/index.md +++ b/draft/7/4d-projection-and-basic-hypercube-twists/index.md @@ -40,7 +40,7 @@ There are 8 facets of a 4-dimensional hypercube, along with the color in standar | `O` | Out | positive W | Pink | | `I` | In | negative W | Purple | -Note: historically, `K` ("kata") has been used instead of `I`, and `A` ("ana") or `T` ("top") have been used instead of `I`. It is recommended to avoid these because it is confusing which one corresponds to which cell. Furthermore, `A` conflicts with 5D notation (`A` for "anterior") and `T` has been reappropriated for general F2L notation (`T` for general "top"). +Note: historically, `K` ("kata") has been used instead of `O`, and `A` ("ana") or `T` ("top") have been used instead of `I`. It is recommended to avoid these because it is confusing which one corresponds to which cell. Furthermore, `A` conflicts with 5D notation (`A` for "anterior"). These also define the standard projection: From 7ae7a7e80ce884829d17e462984c5be7ab53c712 Mon Sep 17 00:00:00 2001 From: HactarCE <6060305+HactarCE@users.noreply.github.com> Date: Fri, 11 Jul 2025 21:58:18 -0400 Subject: [PATCH 6/8] Reword "twist" -> "move" --- .../index.md | 54 +++++++++---------- 1 file changed, 27 insertions(+), 27 deletions(-) diff --git a/draft/7/4d-projection-and-basic-hypercube-twists/index.md b/draft/7/4d-projection-and-basic-hypercube-twists/index.md index fa69cd6..38cac17 100644 --- a/draft/7/4d-projection-and-basic-hypercube-twists/index.md +++ b/draft/7/4d-projection-and-basic-hypercube-twists/index.md @@ -1,4 +1,4 @@ -# Cubing Standard #7: 4D Projection and Basic Hypercube Twists (DRAFT) +# Cubing Standard #7: 4D Projection and Basic Hypercube Moves (DRAFT) Status: `DRAFT` Prescriptive or descriptive: descriptive (this standard attempts to describe existing conventions) @@ -55,48 +55,48 @@ The `O` facet is typically hidden, but the other seven facets are typically visi - `F` may point more left and down - `U` may point more forward -## 7.2 Clockwise Twists +## 7.2 Clockwise Moves -Twists are named using 2, 3, or 4 letters, each corresponding to a facet. All letters are uppercase, with no space or punctuation between them. The first letter indicates which facet is rotated; the remaining letters describe the polytope element that is fixed by the twist. Letters other than the first one may be specified in any order. The twist occurs in a 2D plane, over the minimum nonzero angle necessary to restore the puzzle to its original shape. +Moves are named using 2, 3, or 4 letters, each corresponding to a facet. All letters are uppercase, with no space or punctuation between them. The first letter indicates which facet is rotated; the remaining letters describe the polytope element that is fixed by the move. Letters other than the first one may be specified in any order. The move occurs in a 2D plane, over the minimum nonzero angle necessary to restore the puzzle to its original shape. -| Twist type | Number of letters | Angle | Example | -| ------------ | ----------------- | ----- | ------- | -| Ridge twist | 2 | 90° | `IR` | -| Edge twist | 3 | 180° | `OUR` | -| Corner twist | 4 | 120° | `DUFR` | +| Move type | Number of letters | Angle | Example | +| ----------- | ----------------- | ----- | ------- | +| Ridge move | 2 | 90° | `IR` | +| Edge move | 3 | 180° | `OUR` | +| Corner move | 4 | 120° | `DUFR` | -Rotations appear clockwise when the 4D camera is facing along the vector of the first facet and the 3D camera is facing along the _opposite_ vector from the polytope element described by the second facet. For example, the twist `IR` twists a layer of the `I` facet from positive Z to positive Y, which keeps the vector along the X axis fixed. +Rotations appear clockwise when the 4D camera is facing along the vector of the first facet and the 3D camera is facing along the _opposite_ vector from the polytope element described by the second facet. For example, the move `IR` moves a layer of the `I` facet from positive Z to positive Y, which keeps the vector along the X axis fixed. Examples: -| Twist name | Description | -| ---------- | ------------------------------------------------------------------------ | -| `IR` | `R` twists 90° from `F` to `U` | -| `OUR` | `O` twists 180°, such that `U` and `R` swap and `F` and `B` swap | -| `DUFR` | `D` twists 120° clockwise, such that `F` goes to `I` and `I` goes to `R` | -| | | +| Move name | Description | +| --------- | ------------------------------------------------------------------------ | +| `IR` | `R` twists 90° from `F` to `U` | +| `OUR` | `O` twists 180°, such that `U` and `R` swap and `F` and `B` swap | +| `DUFR` | `D` twists 120° clockwise, such that `F` goes to `I` and `I` goes to `R` | +| | | -In software with mouse controls, these twists are typically executed by right-clicking on the described sticker. For example, `DUFR` is executed by right-clicking on the `D` sticker of the `DUFR` corner piece. +In software with mouse controls, these moves are typically executed by right-clicking on the described sticker. For example, `DUFR` is executed by right-clicking on the `D` sticker of the `DUFR` corner piece. -## 7.3 Double Twists +## 7.3 Double Moves -Ridge twists may be doubled by appending `2` to the move. For example, `DF2` denotes the `DF` twist repeated twice. +Ridge moves may be doubled by appending `2` to the move. For example, `DF2` denotes the `DF` move repeated twice. -Edge twists have order 3 and so do not need to be doubled. +Edge moves have order 3 and so do not need to be doubled. -Corner twists have order 2 and so do not need to be doubled. +Corner moves have order 2 and so do not need to be doubled. -## 7.4 Counterclockwise Twists +## 7.4 Counterclockwise Moves -Twists may be suffixed with `'` to invert them. Alternatively, all but the first letter may be replaced with the letter of the opposite facet. For example, the inverse of `IUR` is `IUR'` or `IDL`. +Moves may be suffixed with `'` to invert them. Alternatively, all but the first letter may be replaced with the letter of the opposite facet. For example, the inverse of `IUR` is `IUR'` or `IDL`. ## 7.5 Layers -Twists may be prefixed with a layer or layer range using SiGN Notation. +Moves may be prefixed with a layer or layer range using SiGN Notation. -## 7.5 Slice Twists +## 7.5 Slice Moves -There are four middle slice layers. Slice twists are constructed from facet twists on a parallel facet according to the following table. +There are four middle slice layers. Slice moves are constructed from facet moves on a parallel facet according to the following table. | Letter | Mnemonic | Parallel facet | | ------ | ------------ | -------------- | @@ -109,7 +109,7 @@ For example, `MD` is equivalent to `2LD` ## 7.6 xyz Notation -Ridge twists may instead be specified using a facet letter followed by a lowercase letter `x`, `y`, or `z`. Each combination of a facet and lowercase `x`/`y`/`z` maps to a ridge turn based on its projection in 3D. In the following table, `_` represents the facet letter. +Ridge moves may instead be specified using a facet letter followed by a lowercase letter `x`, `y`, or `z`. Each combination of a facet and lowercase `x`/`y`/`z` maps to a ridge turn based on its projection in 3D. In the following table, `_` represents the facet letter. | Facet | `_x` | `_y` | `_z` | | ----- | ---- | ---- | ---- | @@ -128,4 +128,4 @@ This notation is generally preferred for puzzle keybinds, for Melinda's 2×2×2 ## 7.6.1 Legacy xyz Notation -Edge and corner twists may be represented using two `x`/`y`/`z` letters, where the last one may be followed by the digit `2` (which applies only to the last letter), but this is discouraged. It is preferred to group multiple ridge twists using parentheses. For example, `Ozx2` should instead be represented as `(Oz Ox2)` or simply `OUFR`. +Edge and corner moves may be represented using two `x`/`y`/`z` letters, where the last one may be followed by the digit `2` (which applies only to the last letter), but this is discouraged. It is preferred to group multiple ridge moves using parentheses. For example, `Ozx2` should instead be represented as `(Oz Ox2)` or simply `OUFR`. From e53eb4d3d3783a8b8f528decf2f0753d0aa31676 Mon Sep 17 00:00:00 2001 From: HactarCE <6060305+HactarCE@users.noreply.github.com> Date: Fri, 11 Jul 2025 22:01:58 -0400 Subject: [PATCH 7/8] Remove mention of legacy xyz notation --- draft/7/4d-projection-and-basic-hypercube-twists/index.md | 4 +--- 1 file changed, 1 insertion(+), 3 deletions(-) diff --git a/draft/7/4d-projection-and-basic-hypercube-twists/index.md b/draft/7/4d-projection-and-basic-hypercube-twists/index.md index 38cac17..bddfc58 100644 --- a/draft/7/4d-projection-and-basic-hypercube-twists/index.md +++ b/draft/7/4d-projection-and-basic-hypercube-twists/index.md @@ -126,6 +126,4 @@ For example, `Fz` is equivalent to `FO`. This notation is generally preferred for puzzle keybinds, for Melinda's 2×2×2×2, and for other physical puzzles. It should be avoided otherwise. -## 7.6.1 Legacy xyz Notation - -Edge and corner moves may be represented using two `x`/`y`/`z` letters, where the last one may be followed by the digit `2` (which applies only to the last letter), but this is discouraged. It is preferred to group multiple ridge moves using parentheses. For example, `Ozx2` should instead be represented as `(Oz Ox2)` or simply `OUFR`. +Moves using xyz notation can be grouped using parentheses. For example `OUFR` is equivalent to `(Oz Ox2)`. From cb588e0ea07be67f8d388a03cd3fe8f51312a093 Mon Sep 17 00:00:00 2001 From: HactarCE <6060305+HactarCE@users.noreply.github.com> Date: Fri, 11 Jul 2025 22:03:03 -0400 Subject: [PATCH 8/8] Remove empty table row --- draft/7/4d-projection-and-basic-hypercube-twists/index.md | 1 - 1 file changed, 1 deletion(-) diff --git a/draft/7/4d-projection-and-basic-hypercube-twists/index.md b/draft/7/4d-projection-and-basic-hypercube-twists/index.md index bddfc58..eb885af 100644 --- a/draft/7/4d-projection-and-basic-hypercube-twists/index.md +++ b/draft/7/4d-projection-and-basic-hypercube-twists/index.md @@ -74,7 +74,6 @@ Examples: | `IR` | `R` twists 90° from `F` to `U` | | `OUR` | `O` twists 180°, such that `U` and `R` swap and `F` and `B` swap | | `DUFR` | `D` twists 120° clockwise, such that `F` goes to `I` and `I` goes to `R` | -| | | In software with mouse controls, these moves are typically executed by right-clicking on the described sticker. For example, `DUFR` is executed by right-clicking on the `D` sticker of the `DUFR` corner piece.