Regular Polytopes · 4D
Tesseract
{4,3,3} · the hypercube
A cube swept through a fourth direction. In perspective it is a cube inside a cube; rotate it through W and the inside turns out.
- Vertices
- 16
- Edges
- 32
- Faces
- 24
- Cells
- 8
Watch it turn through the fourth dimension, hear the chord of its edges, and slice it with our space to see it pass through.
Facts
- Square: 4 corners. Cube: 8. Tesseract: 16. Each dimension doubles them.
- It is bounded by 8 cubes, just as a cube is bounded by 6 squares.
- Turn the dial from 4 to 3 and it collapses into a cube: its shadow along W.
- Its dual is the 16-cell.
History and meaning
Named by Charles Howard Hinton in 1888, who spent years teaching himself to “see” it using coloured cubes. Salvador Dalí crucified Christ on its unfolding net.
Across the dimensions
- Its cell CubeDrag the cube through the fourth direction: the tesseract. Squash W flat and the cube returns.
- Its shadow Rhombic DodecahedronLook at the tesseract corner-first and its shadow is exactly the rhombic dodecahedron.
- Dual 16-Cell
Learn it step by step
- Journey Into the Fourth DimensionStep 3: Now do it again
- Journey FlatlandStep 4: A cube that appears
