Journey 5 of 10 · 9 steps
Flatland
Seeing the fourth dimension in slices
A flat being sees a passing sphere as a circle that grows and shrinks. We can watch 4D shapes pass through our space the same way.
In the app each step moves: figures draw themselves, rise from the page, turn and slice, and the narration can be read aloud. Here they are held still, one picture each.
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Step 1 · Cube
A square that appears
Push a cube face-first through a flat world. A square appears all at once, stays the same, and vanishes. That is all a Flatlander would ever see.
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Step 2 · Cube
A hexagon hiding in a cube
Now push it corner-first. A point, a growing triangle, a perfect hexagon at the middle, then a shrinking triangle. Same cube, a different journey through the plane.
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Step 3 · Tetrahedron
A square in a tetrahedron
A tetrahedron is built from triangles, yet cut edge-first through its middle it leaves a perfect square.
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Step 4 · Tesseract
A cube that appears
One dimension up, a tesseract passing cell-first through our space appears as a cube, stays, and vanishes, just like the square in Flatland.
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Step 5 · Tesseract
Corner first
Turned to meet us corner-first, the slices run from a point through a tetrahedron, an octahedron at the middle, and back. These solids were all hiding inside the tesseract.
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Step 6 · 5-Cell
The 4D triangle
The 5-cell passing through: a tetrahedron grows, its corners are cut off, and it shrinks again.
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Step 7 · 24-Cell
A cuboctahedron at the heart
Through its centre the 24-cell leaves a cuboctahedron, Fuller’s vector equilibrium: twelve spheres around one.
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Step 8 · 600-Cell
A geodesic heart
The 600-cell’s slices are geodesic domes: triangulated shells that grow into a hundred-vertex sphere and shrink away.
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Step 9 · 120-Cell
Soap bubbles
The 120-cell leaves foam: pentagons and hexagons packed on a sphere. A four-dimensional being would see all of it at once. Slice anything in Explore