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: http://gallery.bridgesmathart.org/exhibitions/2015-bridges-conference/monkeys

• 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.

• http://vihart.com
• http://andreahawksley.com
• http://www.segerman.org/
• http://willsegerman.com
• http://www.marctenbosch.com
• https://github.com/MozVR/vr-web-examples/tree/master/threejs-vr-boilerplate
• http://threejs.org