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Regular Polytopes · 4D

120-Cell

{5,3,3} · the dodecaplex

120-Cell, drawn as a glowing line figure

One hundred and twenty dodecahedra wrapped into a hypersphere. The crown jewel of four-dimensional geometry.

Vertices
600
Edges
1200
Faces
720
Cells
120

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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

  • It is the 4D dodecahedron, and the dual of the 600-cell.
  • Every face is a pentagon; φ runs through every coordinate.
  • Stereographically projected, its dodecahedral cells form nested soap-bubble shells.

History and meaning

H. S. M. Coxeter, who devoted a lifetime to these shapes, called it one of the most beautiful objects in mathematics.

Across the dimensions

  • Its cell DodecahedronOne hundred and twenty dodecahedra close into a hypersphere: the 120-cell.
  • Dual 600-Cell

Learn it step by step

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