Curtis L Palmer

Edmonton, Alberta, Canada
Twenty seven years ago I affixed 3 mirrors to a computer monitor aligned with the with central angles of the icosahedron. A triangular section of the monitor became a segment of a virtual spherical icosahedron when viewed from the front.

I applied a random graphics routine as the Dynamic Texture Map.

Randomness instantaneously became order, in the round!

Recently I found a way to use 3D modelling software to reproduce the dynamic kaleidoscopic effect without the use of any mirrors. A flurry of animating has begun. Alas the software fails if I ask of it too many frames at a time. I am too old for BUGS!

Perseverance furthers.

Icosahedra Cyclonified
Curtis L Palmer
A method for kaleidoscopically painting an Icosahedron is illustrated by two clips. In each, an array of icosahedral simplex components is painted with an icosahedral Cyclon in rotation (cf. Palmer Bridges past). The Cylon used as a texture map is reproduced as the end frame of my movie. Colours have been modified.

With 3,600 frames (0.1 degree rotation per frame) produces a smooth full rotation that will loop with no cusp.

Images in each row of Clip 1 are aligned to the icosahedron's axes of symmetry: Edge, Face Vertex. They are the behind the scenes components of icosahedral symmetry simplexes. What I call: circumsphere, screens, altitudes, bases and hypoteni are surfaces produced by cutting along the planes of symmetry.

Clip 2 shows a rotated close up of clip 1, the spherical icosahedra paired with their 'screens' counterpart.

The corona virus's capsids have icosahedral symmetry.

"What immortal hand or eye could frame thy fearful symmetry?" Blake.