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Monkey See, Monkey Do

Monkeys arranged symmetrically in 4D space, in VR.

The sculptures visualise different 4D symmetry groups. A monkey motif is placed in each cube, octahedron or dodecahedron of the 8-, 24- or 120-cell, giving objects with symmetry groups the 8-element quaternion group, the binary tetrahedral group, and the binary icosahedral group respectively. The designs are radially projected to the 3-sphere then stereographically projected to 3-space. The VR experience animates each of these, showing one generator of each symmetry group. The virtual monkeys are coloured by an algorithm based on the Hopf fibration from the 3-sphere to the 2-sphere, which is then embedded in the RGB colour cube.

Monkey See, Monkey Do in the Bridges Math Art Exhibit 2015:

Useful commands

  • 8-cell: 1
  • 24-cell: 2
  • 24-cell dual: 3
  • 24-cell and dual: 4
  • 48-cell: 5
  • 120-cell: 6
  • fullscreen: tap or click
  • rotation: w a s d q e or headset rotation in webVR or mobile device rotation
  • movement: arrow keys

By Vi Hart, Andrea Hawksley, Henry Segerman, and Will Segerman, using Marc ten Bosch's 4D graphics shader, Mozilla's webVR stuff, and threejs.


monkeys arranged symmetrically in 4D space, in VR.



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