Welcome to the icosahedron home page
What is the best way to pixelize a sphere? This question
occurs in many practical applications, for instance when making
maps (of the earth or the celestial sphere) and when doing
numerical integrals over the sphere.
This web site contains source code and documentation
for the method depicted above, which involves inscribing the sphere
in a regular icosahedron and then equalizing the pixel areas.
You can get the 1.3MB uncompressed
postscript file by clicking
For a public domain FORTRAN implementation of the method,
if you are interested in
other research of mine.
Below is some more information about the method paper.
An icosahedron-based method for pixelizing the celestial sphere
For power spectrum estimation
it's important that the pixelization
of a CMB sky map be
smooth and regular to high degree.
With this criterion in mind
the "COBE sky cube" was defined.
This paper has as central theme
to further improve on this elegant scheme
which uses a cube as projective base
- here an icosahedron is used in its place.
Although the sky cube is excellent,
a further reduction of 20 percent
of the number of pixels can be obtained
while the pixel distance is maintained,
and without any degradation
of accuracy for integration.
The pixels are rounder in this scheme where
they are hexagonal rather than square,
and the faces are small in this implementation
which simplifies area-equalization.
The reason distortion is lessened is that
the faces are smaller and therefore more flat.
To use the method, you can get
a FORTRAN code from the Internet.
Published in ApJ Lett, 470, L81-L84 (1996)
This site also contains the latest versions of a paper that is referenced in
Tegmark, Taylor & Heavens 1996.
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This page was last modified July 1, 1998.