AI Generated finetuned for the visualisation and not code quality.

Interactive C + Raylib viewer for the 600-cell, a regular 4D polytope. The app generates the polytope's 4D vertices, connects nearest-neighbour edges, rotates the shape through multiple 4D planes, projects it down into 3D and then 2D, and lets you explore a highlighted W-slice of the structure in real time.

• Generates the 120 canonical 4D vertices of the 600-cell
• Builds edge connectivity by detecting the shortest 4D neighbour distance
• Animates simultaneous rotations in the XY, XZ, XW, YZ, YW, and ZW planes
• Projects the rotating 4D shape into 3D and then onto the 2D window
• Colors points and edges by their current W coordinate
• Highlights a configurable W slice so you can see which parts of the polytope sit near a chosen hyperplane
• Lets you orbit the projected view in 3D and manually drag the XW and YW rotations
• Shows hover details for vertices and edges, including degree, current 4D coordinates, and projected edge length

flowchart LR
    A["4D Vertex Families<br/>8 axis points<br/>16 sign points<br/>96 golden-ratio points"]
    B["Nearest-Neighbour Edge Build<br/>connect shortest 4D pairs"]
    C["Animated 4D Rotation<br/>XY XZ XW YZ YW ZW"]
    D["4D -> 3D Projection<br/>controlled by wDist"]
    E["3D Orbit View<br/>yaw + pitch from left-drag"]
    F["3D -> 2D Projection<br/>controlled by zDist"]
    G["Screen Render<br/>edges, points, hover inspector"]

    A --> B --> C --> D --> E --> F --> G

    classDef geo fill:#16324f,stroke:#8fd3ff,color:#f4fbff,stroke-width:2px;
    classDef motion fill:#3c1642,stroke:#f08bd7,color:#fff4fb,stroke-width:2px;
    classDef proj fill:#234f1e,stroke:#9be27f,color:#f6fff4,stroke-width:2px;
    classDef render fill:#5b3a00,stroke:#ffd166,color:#fff9ec,stroke-width:2px;

    class A,B geo;
    class C motion;
    class D,E,F proj;
    class G render;

flowchart TB
    W["Chosen W Slice<br/>sliceW +/- sliceThickness"]
    P["Points near the slice<br/>larger radius + brighter glow"]
    E["Edges near the slice<br/>extra width + alpha boost"]
    C["Hue by W value<br/>blue/cyan through warmer tones over time"]
    H["Hover inspector<br/>vertex degree, 4D coords, edge metrics"]

    W --> P
    W --> E
    C --> P
    C --> E
    P --> H
    E --> H

    classDef slice fill:#1d3557,stroke:#8ecae6,color:#f1f8ff,stroke-width:2px;
    classDef focus fill:#5a189a,stroke:#f72585,color:#fff5ff,stroke-width:2px;
    classDef info fill:#264653,stroke:#e9c46a,color:#fffbea,stroke-width:2px;

    class W slice;
    class P,E,C focus;
    class H info;

• Point color: encodes the current W coordinate
• Point size: grows when a vertex is close to the active W slice
• Edge brightness: increases when an edge sits near the slice or is hovered
• Hover focus: unrelated geometry is dimmed so local structure is easier to read
• Bottom info card: switches between vertex-specific and edge-specific measurements

• q: quit
• 1: open the main 600-cell viewer
• 2: open page 2 placeholder
• space: pause or resume animation

• mouse wheel: zoom in or out
• left drag: orbit the 3D projection
• right drag: manually adjust XW and YW 4D rotation
• hover vertex: inspect degree, W, slice delta, and current 4D coordinates
• hover edge: inspect endpoint ids, 4D edge length, projected length, and mean W

• View and styling: Zoom, Line Width, Point Size, Edge Alpha
• Projection: W Distance, Z Distance
• Rotation rates: rXY, rXZ, rXW, rYZ, rYW, rZW
• Slice controls: Slice W, Slice Width, Slice Boost

The most useful mental model is that the app is not only drawing a spinning wireframe. It is also giving you a moving spotlight through the fourth dimension:

• sliceW picks a target location along the W axis
• sliceThickness defines how much nearby geometry counts as "in slice"
• sliceBoost makes that neighbourhood stand out visually

This makes it easier to see how a 4D object changes as different parts of it pass near a chosen hyperplane.

• raylib
• pkg-config
• a C compiler such as cc or clang

make
make run