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Regular Polytopes · 4D

5-Cell

{3,3,3} · the 4D simplex

5-Cell, drawn as a glowing line figure

Five points, each joined to every other: the simplest shape in four dimensions, bounded by five tetrahedra.

Vertices
5
Edges
10
Faces
10
Cells
5

Open in SacredForm

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

  • Point → segment → triangle → tetrahedron → 5-cell: add one point, join it to all.
  • Every pair of its 5 vertices is joined, like a pentagram in 2D.
  • It is its own dual.

Across the dimensions

  • Its cell TetrahedronAdd a fifth point in the fourth direction, joined to all four: the 5-cell, with this tetrahedron as one of its five cells.
  • Dual Itself: it is self-dual.

Learn it step by step

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