LiveGraphics3D e

the LiveGraphics3D applet and interesting sites

08-02-2009

How to leave this page? Good question!

Of course you can use the "previous page" button or return to the summary, but you may also discover other sites devoted to polyhedra by clicking on one of the labels on the globe.
(Data extracted by Martin Kraus from the Mathematica package Miscellaneous `WorldData`).
The zoom function let you better distinguish the labels.

This Java applet has been developed by Martin Kraus; it allows you to move 3D graphics with your mouse.
Thanks to Martin for his help, especially for the parameterised animations.

If an applet refuses to start, reload the page from the address bar to reload the Java code.

How to use LiveGraphics3D:

As soon as the pointer enters an applet zone the applet takes the focus and keeps it; to restore the focus to the HTML page (and reactivate keyboard shortcuts) one must click on the page outside of an applet zone.

Below "left", "right" points out the mouse's button to hold, and "Shift", "Ctrl" points out the key to maintain in addition.

drag-left to rotate the globe around an axis in the picture; if you release the button while dragging the rotation continues (spin) as long as the pointer remains on the picture (it resumes when the pointer comes back on it),
Shift-drag-left horizontally to rotate around an axis perpendicular to the picture.
Shift-drag-left vertically to zoom,
Ctrl-drag-left vertically to change the focal length,
the "F" key toggles between normal and "wire view" (only the edges are displayed),
drag-right vertically to suppress faces of a polyhedron,
the "S" key toggles between single and stereo picture; Ctrl-drag-left horizontally to change strength of stereo effect,
the pointer starts a possible animation, and stops it when it leaves the picture; a left double click stops or restarts the animation: when stopped, drag-right horizontally controls the animation,
some drawings may be dynamically modified: stop the motion (click anywhere on the picture), then left-drag one of the big points to move it (a little square centred on the point allows to identify easily such a point).

My favourite sites and programs (cf labels on the globe):

New York		Hundreds of polyhedra and sculptures by George W. Hart (needs a VRML plug-in) and his polyhedron generator using John Conway's notation.
Brisbane		Many very nice POV-Ray images with the data used to define the displayed polyhedron (Object File Format).
Illinois		The polyhedra in Eric W. Weisstein's MathWorld encyclopedia (Wolfram) with LiveGraphics3D.
Erlangen		The regular and normal kaleidocycles' theory by Marcus Engel, with a nice animation and video clips. (You can download an "off line" version of the animation.)
Zaragoza		Study of an IsoAxis object with a video clip (in Spanish, English and French translations in progress).
Brussels		The course by Xavier Hubaut: polyhedra and groups of isometries (in French).
Rennes		Nice pages by Nicolas Hannachi, especially about "kissing circles" and "kissing spheres" (in French).

Terrace		Poly is a must to begin with convex polyhedra.
Melbourne		Great Stella is a very complete program to explore the polyhedra world and create your own models; a paper by the author, published in Symmetry: Culture and Science journal, summarizes the many features offered by Stella, and takes stock up of the research in polyhedra theory. Stella4D is the ultimate tool for 3D or 4D investigation written by Robert Webb.

To produce the images animated with LiveGraphics3D from Martin Kraus (Germany) I used Mathematica, Great Stella by Robert Webb (Australia), Hedron by Jim McNeill (United Kingdom) and the polyhedron generator (John Conway's notation) by George W. Hart (USA).
Data from Eric Hackenholz, Christian Camalon and Hubert Martineau (Reunion Island, France), Xavier Hubaut (Free University of Brussels), Eric W. Weisstein (Wolfram Research, USA), George W. Hart (New York), Guy Inchbald (United Kingdom), Nicolas Hannachi (France) and Maurice Starck (New-Caledonia, France).