diff --git a/docs/puzzles/.nav.yml b/docs/puzzles/.nav.yml index e07b1381c..b4fac45d5 100644 --- a/docs/puzzles/.nav.yml +++ b/docs/puzzles/.nav.yml @@ -1,7 +1,5 @@ nav: +- 4D+: 4d-plus - physical -- 3x3x3.md -- 2x2x2x2.md -- 3x3x3x3.md -- nxnxnxn.md -- "*" +- circle +- tilings diff --git a/docs/puzzles/3x3x3.md b/docs/puzzles/3x3x3.md index 36a390a1b..bf5f9ca11 100644 --- a/docs/puzzles/3x3x3.md +++ b/docs/puzzles/3x3x3.md @@ -1,3 +1,7 @@ +--- +hide: [navigation, toc] +--- + # 3×3×3 There's not much we can say about the traditional Rubik's cube that hasn't already been said on [Wikipedia](https://en.wikipedia.org/wiki/Rubik%27s_Cube) or the [Speedsolving.com Wiki](https://www.speedsolving.com/wiki/index.php?title=Rubik%27s_cube_(puzzle_type)). diff --git a/docs/puzzles/2x2x2x2.md b/docs/puzzles/4d-plus/2x2x2x2.md similarity index 100% rename from docs/puzzles/2x2x2x2.md rename to docs/puzzles/4d-plus/2x2x2x2.md diff --git a/docs/puzzles/3x3x3x3.md b/docs/puzzles/4d-plus/3x3x3x3.md similarity index 100% rename from docs/puzzles/3x3x3x3.md rename to docs/puzzles/4d-plus/3x3x3x3.md diff --git a/docs/puzzles/3x3x3x3x3.md b/docs/puzzles/4d-plus/3x3x3x3x3.md similarity index 100% rename from docs/puzzles/3x3x3x3x3.md rename to docs/puzzles/4d-plus/3x3x3x3x3.md diff --git a/docs/puzzles/4d-skewb.md b/docs/puzzles/4d-plus/4d-skewb.md similarity index 100% rename from docs/puzzles/4d-skewb.md rename to docs/puzzles/4d-plus/4d-skewb.md diff --git a/docs/puzzles/hypercuboids.md b/docs/puzzles/4d-plus/hypercuboids.md similarity index 100% rename from docs/puzzles/hypercuboids.md rename to docs/puzzles/4d-plus/hypercuboids.md diff --git a/docs/puzzles/4d-plus/index.md b/docs/puzzles/4d-plus/index.md new file mode 100644 index 000000000..44eb63469 --- /dev/null +++ b/docs/puzzles/4d-plus/index.md @@ -0,0 +1,7 @@ +# Higher-Dimensional Puzzles + +In hypercubing, our primary focus is generalizing the notion of a twisty puzzle beyond 3D space. The best introduction to hypercubing is the standard [3×3×3×3](/puzzles/3x3x3x3.md) 4D Rubik's cube. + +The recommended place to solve all 4D+ puzzles is [Hyperspeedcube](https://github.com/HactarCE/Hyperspeedcube) after the v2.0 update. + +See the navigation sidebar for a list of puzzles that have wiki pages. \ No newline at end of file diff --git a/docs/puzzles/nxnxnxn.md b/docs/puzzles/4d-plus/nxnxnxn.md similarity index 100% rename from docs/puzzles/nxnxnxn.md rename to docs/puzzles/4d-plus/nxnxnxn.md diff --git a/docs/puzzles/index.md b/docs/puzzles/index.md deleted file mode 100644 index cd5c0ccba..000000000 --- a/docs/puzzles/index.md +++ /dev/null @@ -1,5 +0,0 @@ -# Puzzles - -In hypercubing, we generalize the notion of a twisty puzzle beyond 3D space. The best introduction to hypercubing is the standard [3×3×3×3](/puzzles/3x3x3x3.md) 4D Rubik's cube. - -See the navigation sidebar for a list of puzzles that have wiki pages. diff --git a/docs/puzzles/hemimegaminx.md b/docs/puzzles/tilings/hemimegaminx.md similarity index 97% rename from docs/puzzles/hemimegaminx.md rename to docs/puzzles/tilings/hemimegaminx.md index 609a8213e..db9206e70 100644 --- a/docs/puzzles/hemimegaminx.md +++ b/docs/puzzles/tilings/hemimegaminx.md @@ -1,7 +1,7 @@ # Hemimegaminx !!! info inline end "Hemimegaminx" - ![Hemimegaminx in MagicTile](https://assets.hypercubing.xyz/img/virt/mt_hemimega.png) + ![Hemimegaminx in MagicTile](https://assets.hypercubing.xyz/img/virt/tilings/mt_hemimega.png) **Shape:** [Hemi-dodecahedron](https://polytope.miraheze.org/wiki/Hemidodecahedron) diff --git a/docs/puzzles/tilings/index.md b/docs/puzzles/tilings/index.md new file mode 100644 index 000000000..3b4d9feb8 --- /dev/null +++ b/docs/puzzles/tilings/index.md @@ -0,0 +1,24 @@ +# Tiling Puzzles + +Tiling puzzles are puzzles created from cutting regular tilings in flat euclidean or hyperbolic space. They are primarily simulated on [MagicTile](http://roice3.org/magictile/). + +## Topological Spaces + +The familiar 3^3^ Rubik's cube lives in spherical space, with the cube having a Schläfli symbol of {$4,3$}. This means that 3 squares (4 edges) meet at a vertex. This can be abstracted - the Schläfli symbol {$4,4$} is 4 squares meeting at each vertex, something that cannot be represented in spherical space. Instead, it is an infinite tiling of the Euclidean plane. The tiling {$4,5$} is too big to fit within even the Euclidean plane, and resides in hyperbolic space. Below is a visualization of the above tilings. + +!!! example "Demonstration of square tilings in different spaces ([Roice Nelson and Henry Segerman, 2016](https://arxiv.org/abs/1511.02851))" + ![Square tilings {4,3}, {4,4}, and {4,5}](https://assets.hypercubing.xyz/img/virt/tilings/square_tilings.png) + +!!! info inline end "Hemimegaminx, a projective plane puzzle" + ![Hemimegaminx in MagicTile](https://assets.hypercubing.xyz/img/virt/tilings/mt_hemimega.png) + +The [projective plane](https://en.wikipedia.org/wiki/Projective_plane) puzzles in MagicTile are spherical puzzles where the two hemispheres are mapped to each other. The point directly opposite each point on the other hemisphere is the same point. Looking at the hemimegaminx from inside the sphere, the point you are looking at and the point at infinity right behind you are the same. + +The torus and Klein bottle puzzles are Euclidean plane puzzles that emerge from the same quotient, but with slightly different properties. The copies of the faces on the torus puzzles all rotate the same way, but the faces on the Klein bottle puzzles alternate their rotation due to the differences in topology. Mathologer has an [introduction](https://www.youtube.com/watch?v=DvZnh7-nslo) to Klein bottle puzzles. + +## Quotienting + +We can cut these tilings (similar to cutting a cube to make a Rubik's cube) to make puzzles. However, the infinite tilings have to be made finite through quotienting - the act of taking a repeating pattern to create a smaller quotient space. Multiple quotients can exist for the same tiling. + +!!! example "Two different puzzles created from different quotients of the hex tiling (MagicTile)" + ![Hex tiling puzzles](https://assets.hypercubing.xyz/img/virt/tilings/mt_hex_tilings_quotients.png) \ No newline at end of file diff --git a/docs/puzzles/tilings/klein_quartic.md b/docs/puzzles/tilings/klein_quartic.md new file mode 100644 index 000000000..c44767efb --- /dev/null +++ b/docs/puzzles/tilings/klein_quartic.md @@ -0,0 +1,34 @@ +--- +title: Klein Quartic +--- + +# Canon-Cut Klein Quartic + +!!! info inline end "Canon-Cut Klein Quartic" + ![Klein quartic in MagicTile](https://assets.hypercubing.xyz/img/virt/tilings/mt_kq.png) + + **Shape:** [Klein Quartic](https://en.wikipedia.org/wiki/Klein_quartic) + + **Pieces:** 24 1c, 84 2c, 56 3c + +The canon-cut klein quartic is a twisty puzzle cut from the 24-color quotient of the {$7,3$} who exists in hyperbolic space. + +It has 3 "mutually opposite" sides, meaning each face has 2 others that is as far away from it as can be. This means that the entire puzzle can be split into 3 groups of 8 heptagons (a central one surrounded by its 7 neighbors). This property does not exist on spherical puzzles, as you can always separate one hemisphere from the other. + +## Speedsolving Method + +The speedsolving method utilizes the 3-sided nature of the puzzle. + +Solve the cross on one face and all its F2L-a pairs. + + + +Solve the cross of one of the two opposite faces and all its F2L-a pairs. + + + +Solve all pieces between the two sections you just solved (everything except for the remaining opposite side and its neighbors). + + + +Solve the last section like Megaminx S2L and LL. \ No newline at end of file diff --git a/mkdocs.yml b/mkdocs.yml index c3201d0c4..aead29f3e 100644 --- a/mkdocs.yml +++ b/mkdocs.yml @@ -156,6 +156,13 @@ plugins: "leaderboards/solvers/messil.md": "https://lb.hypercubing.xyz/solver?id=56" "leaderboards/solvers/voytxt.md": "https://lb.hypercubing.xyz/solver?id=57" "leaderboards/solvers/emca.md": "https://lb.hypercubing.xyz/solver?id=58" + "puzzles/hemimegaminx.md": "puzzles/tilings/hemimegaminx.md" + "puzzles/2x2x2x2.md": "puzzles/4d-plus/2x2x2x2.md" + "puzzles/3x3x3x3.md": "puzzles/4d-plus/3x3x3x3.md" + "puzzles/3x3x3x3x3.md": "puzzles/4d-plus/3x3x3x3x3.md" + "puzzles/4d-skewb.md": "puzzles/4d-plus/4d-skewb.md" + "puzzles/hypercuboids.md": "puzzles/4d-plus/hypercuboids.md" + "puzzles/nxnxnxn.md": "puzzles/4d-plus/nxnxnxn.md" hooks: - hooks/feature_matrix.py - hooks/symbol_hooks.py