Retrograde Rotation Illusions in Turntable Animations of Concentric Icosahedral Domains

Curtis Palmer
Proceedings of Bridges 2013: Mathematics, Music, Art, Architecture, Culture (2013)
Pages 491–494 Short Papers


I have constructed for comparison two sets of computer models of the icosahedron, dodecahedron and icosidodecahedron using 3D modeling software. One set uses coordinates attributed to Hess [1] and the other fits within a unit radius circumsphere. Each polyhedrons' sets of vertices, edges, faces, bounding boxes, polysurface and circumsphere are constructed upon named layers that can be turned on or off within a tree of layers. These trees of data constitute the Taublock and the Uniblock. Three copies of each block are scaled proportional to a golden ratio geometric series: τau, 1, 1/τau. These triads are used to populate turntable animations with varying display parameters for visual effect. With apparent motion and programmatic selection of layers and display attributes these objects, alone and in combination, provide for many visual surprises such as retrograde rotation illusions and the appearance of phantom faceted polyhedra.