Hypercube

Basic Controls

• DragRotate the shape in XZ / YZ planes
• Scroll / ZoomZoom in and out. The Zoom slider does the same.
• SpeedRate of auto-rotation in the extra-dimensional planes (W through C). Set to 0 to freeze.
• FadeHow strongly depth dims back-facing edges. Higher values make 3D structure more readable against the background.
• 1D – 9DMorph the shape into that dimension, one step at a time

Standard Shapes

• 1D — Line2 vertices, 1 edge
• 2D — Square4 vertices, 4 edges
• 3D — Cube8 vertices, 12 edges
• 4D — Tesseract16 vertices, 32 edges
• 5D — Penteract32 vertices, 80 edges
• 6D — Hexeract64 vertices, 192 edges
• 7D — Hepteract128 vertices, 448 edges
• 8D — Octeract256 vertices, 1024 edges
• 9D — Enneract512 vertices, 2304 edges

Visual Options

• PerspectiveEach higher dimension is foreshortened like depth
• OrthographicParallel projection — shows true symmetry
• Color AxesEdges colored by axis: X Y Z W V U A B C
• Fill PanelsFill each square face with translucent shading for a solid model look. Front-facing panels are brighter.
• OpacityCycles through five panel transparency levels: Ghost, Low, Mid, High, Solid. Only active when Fill Panels is on.
• Vertex DotsRender a glowing dot at every vertex, scaled by perspective depth. Spectacular in 5D+.
• CoordsHover near any vertex to see its raw nD coordinates before rotation.
• Lock W – CFreeze auto-rotation on that axis so you can study a fixed orientation. Only appears when the corresponding dimension is active.
• iToggles a live info card (top-left) that explains in plain language exactly what you are viewing — shape, projection mode, and every active feature.

Modes

• LoopAuto-cycles 1D → 9D → 1D continuously at double morph speed.
• GyroOn mobile: tilt the phone to rotate the shape. iOS will ask for permission.
• SliceReal-time cross-section: a hyperplane cuts through the shape along its outermost dimension. The slider moves the cutting plane from −1 to +1. Hit Sweep to animate the plane bouncing end-to-end — a 4D tesseract rotated 45° produces the sequence point → tetrahedron → octahedron → tetrahedron → point.
• Draw ShapeSketch any 2D polygon on the canvas, then extrude it into 3D, 4D, and beyond — the same way a square extrudes into a cube. Click to place vertices; click the first point (orange ring) to close. Use the dim buttons to extrude further.
• TrailsEach vertex leaves a fading path as the shape rotates. In higher dimensions the curves are projections of trajectories through SO(n) — geometry that has no analogue in 3D intuition.
• DualOverlays the dual polytope (cross-polytope / hyperoctahedron) in amber. The dual of a cube is an octahedron; the dual of a 4D tesseract is the 16-cell. Both rotate together, sharing the same axes.

About

An n-dimensional hypercube is formed by extruding an (n−1)-dimensional cube along a new perpendicular axis. Each step doubles the vertices. Shapes are mathematically exact — rendered via cascading perspective projection through each spatial dimension. Custom shapes use the Cartesian graph product to extrude any polygon into higher dimensions.