Uploaded April 2018 | Updated September 2026, 2 weeks ago
This video shows the Fourier transform of the vertices of a regular icosahedron (i.e., of a sum of Dirac δ distributions, one at each vertex of the icosahedron) as a 3D function viewed through 2D slices whose direction is a Coxeter plane of the icosahedron.
Positive values are represented as shades of gray and negative values as shades of blue. The origin is in the center of the frame at the middle of the video (24″).
The vertices are at: (0, ±1, ±ϕ), (±1, ±ϕ, 0), (±ϕ, 0, ±1), where ϕ is the golden ratio, and the plane sections are orthogonal to (0,2+ϕ,1+3ϕ).
(The earlier video youtube.com/watch?v=uyitkl00Ey4 shows the same thing but with a different slicing and a different color gradient.)
This video shows the Fourier transform of the vertices of a regular icosahedron (i.e., of a sum of Dirac δ distributions, one at each vertex of the icosahedron) as a 3D function viewed through 2D slices whose direction is a Coxeter plane of the icosahedron.
Positive values are represented as shades of gray and negative values as shades of blue. The origin is in the center of the frame at the middle of the video (24″).
The vertices are at: (0, ±1, ±ϕ), (±1, ±ϕ, 0), (±ϕ, 0, ±1), where ϕ is the golden ratio, and the plane sections are orthogonal to (0,2+ϕ,1+3ϕ).
(The earlier video youtube.com/watch?v=uyitkl00Ey4 shows the same thing but with a different slicing and a different color gradient.)
