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: http://gallery.bridgesmathart.org/exhibitions/2015-bridges-conference/monkeys
- 24-cell dual:
- 24-cell and dual:
w a s d q eor
headset rotation in webVRor
mobile device rotation
By Vi Hart, Andrea Hawksley, Henry Segerman, and Will Segerman, using Marc ten Bosch's 4D graphics shader, Mozilla's webVR stuff, and threejs.