The edge-skeleton of some uniform polyhedra can be connected by regular polygons in different ways. This creates "regiments" of very interesting new polyhedra, all being derived from their "colonel". The number of "facetings" in the regiments depends on the symetry of their colonel. Dr. Richard Klitzing has taken the task to discover all facetings of the uniform polyhedra and to enumerate all of those which have at least a rotational symmetry of an order larger than 2.
With the help of the software "hedron" by Jim McNeill Klitzing created the VRML-files. To watch them you need the Cortona3D Viewer. Pictures and VRML-files are shown with kind permission.
The nomenclature of the polyhedra depends of the number of the polygons: The 6-15-5-1 from the sidtid-group is made of 6 pentagrams, 15 triangles, 5 squares and 1 pentagon, in the 7-10-11-15 from the raded-group there are 7 pentagrams, 10 squares, 11 pentagons and 15 hexagons. The system of short names (co, id, raded, gidrid...) was created by J. Bowers.
Colonel Click on the colonel to get to the regiment. |
Example of a faceting Click on the example's picture for VRML-solid, on the text for VRML-frame |
 |
 |
 |
 |
 |
 |
 |
 |
 |
 |
 |
 |
 |
 |
 |
 |
 |
 |
 |
 |
 |
 |
 |
 |
 |
 |
 |
|
 |
 |
 |
 |
