Hypercubers · cryofractal · Aug 14, 2026 · Aug 14, 2026 · Aug 14, 2026 · Aug 14, 2026
diff --git 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
@@ -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 → docs/puzzles/4d-plus/2x2x2x2.md b/docs/puzzles/2x2x2x2.md → docs/puzzles/4d-plus/2x2x2x2.md
diff --git a/docs/puzzles/3x3x3x3.md → docs/puzzles/4d-plus/3x3x3x3.md b/docs/puzzles/3x3x3x3.md → docs/puzzles/4d-plus/3x3x3x3.md
diff --git a/docs/puzzles/3x3x3x3x3.md → docs/puzzles/4d-plus/3x3x3x3x3.md b/docs/puzzles/3x3x3x3x3.md → docs/puzzles/4d-plus/3x3x3x3x3.md
diff --git a/docs/puzzles/4d-skewb.md → docs/puzzles/4d-plus/4d-skewb.md b/docs/puzzles/4d-skewb.md → docs/puzzles/4d-plus/4d-skewb.md
diff --git a/docs/puzzles/hypercuboids.md → docs/puzzles/4d-plus/hypercuboids.md b/docs/puzzles/hypercuboids.md → docs/puzzles/4d-plus/hypercuboids.md
diff --git a/docs/puzzles/4d-plus/index.md 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.
diff --git a/docs/puzzles/nxnxnxn.md → docs/puzzles/4d-plus/nxnxnxn.md b/docs/puzzles/nxnxnxn.md → docs/puzzles/4d-plus/nxnxnxn.md
diff --git a/docs/puzzles/index.md b/docs/puzzles/index.md
diff --git a/docs/puzzles/hemimegaminx.md → docs/puzzles/tilings/hemimegaminx.md b/docs/puzzles/hemimegaminx.md → 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
@@ -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)
diff --git a/docs/puzzles/tilings/klein_quartic.md 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.
+
+<object alt="White cross + F2L" data="https://assets.hypercubing.xyz/img/virt/tilings/cckq_speedsolving_method/cckq_step1.png" height="300"></object>
+
+Solve the cross of one of the two opposite faces and all its F2L-a pairs. 
+
+<object alt="Teal cross + F2L" data="https://assets.hypercubing.xyz/img/virt/tilings/cckq_speedsolving_method/cckq_step2.png" height="300"></object>
+
+Solve all pieces between the two sections you just solved (everything except for the remaining opposite side and its neighbors).
+
+<object alt="S2L + LL" data="https://assets.hypercubing.xyz/img/virt/tilings/cckq_speedsolving_method/cckq_step3.png" height="300"></object>
+
+Solve the last section like Megaminx S2L and LL.
diff --git 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