What is this about 20-sided turnovers?

Although many browsers allow one to look at calculated 3D objects from any direction, displaying experimental data on a real-world object from all directions is more problematic. One solution is a template of 20 HTML files which allows one to "navigate" a set of images taken along the 20 face normals of an icosahedron using most any graphical browser. If you download the 20 HTML files here into a directory, then you need only supply 20 large (c0...c9, e0...e9) and 20 small (c0x...c9x, e0x...e9x) GIF or JPG images, taken of your object from the appropriate directions.

Fig. 1: An unfolded icosahedron, with the faces labeled according to the scheme used here

It is possible to take pictures from the required angles* for large vertical prolate (i.e. elongate) objects even if they are unmovable, by climbing ladders and lying on the floor with a sufficiently wide angle lens, as illustrated in the electron microscope example on these pages. One then need only digitize the images, and give them filenames according to the direction they were taken.

We envision uses in showing equipment, in showcasing the interior of rooms with a wide-angle lens,and possibly for showing experimental electron diffraction Kikuchi maps of interesting crystals, quasi-crystals, and their approximates. If there is interest in more on the strategies we've used to aquire images for use with such templates, drop me a note*. We also have some algorithms for determining the 3D convex-envelope coordinates, and volume, of objects so imaged.

Cheers. /philf :)

* In terms of the usual spherical-coordinate angles phi (azimuth) and theta (tilt), the even equatorial views {e0, e2, e4, e6, e8} have tilts from z-positive (e.g. an arbitrarily chosen north pole) of 100.8 degrees, and azimuth values from an arbitrarily chosen x-direction of {0, 72, 144, -144, -72}, while the even cap views {c0, c2, c4, c6, c8} have the same azimuths, but tilts of 142.6 degrees from z-positive. The odd views (i.e. those above northern hemisphere sites if one were envisioning a globe) have azimuths from x-positive of {36, 108, 180, -108, -36}, with equatorial tilts of 79.2 degrees, and cap tilts of 37.4 degrees, all again from z-positive (e.g. the north pole).

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