Collection of forms resulting from all the combinations of the Platonic and Catalan polyhedra
which characterize the m 3 5
icosahedral point group
Dip.Te.Ris., Universita' di Genova, Italy
(E-mail address: email@example.com)
Tested with Internet Explorer 7, Mozilla Firefox 3, Opera 9.64 and
Google Chrome at 1024x768 and 1280x1024 pixels
All the images have been generated by SHAPE 7.0, a software program for
drawing the morphology of crystals, distributed by Shape Software
Hovering with the mouse on each image, the symbol of a pointer appears:
if your web browser is set up to visualize VRML files, by clicking with
the left button of the mouse it should be possible to visualize in a new
window the corresponding dynamic image, that can be enlarged, rotated,
shifted... Cortona 3D Viewer is a good Web3D visualizer that can be
downloaded from here
at present it is working also with the updated versions of the main browsers.
As already pointed out in two previous papers
[1,2], all the icosahedral compound forms, and in particular the ones belonging to the
5 point goup, can be
derived from seven single forms, corresponding to two Platonic and five Catalan polyhedra.
The two Platonic polyhedra are the dodecahedron and the icosahedron: both are
characterized by Miller's indices having a fixed value. The same holds true for the rhomb-triacontahedron,
a Catalan polyhedron dual of a quasi-regular Archimedean polyhedron, the icosidodecahedron.
Conversely, the indices of the other four forms can assume variable values, in the intervals defined in the following table.