LiveGraphics3D

the LiveGraphics3D applet and interesting sites

16-03-2024

How to leave this page? Good question!

Of course you can use the "previous page" button or return to the home page, 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 `WorldData`.)

The zoom function let you better distinguish the labels.
If an applet refuses to start, reload the page with Ctrl-Shift-R.

This Java applet, developed by Martin Kraus, allows you to move 3D graphics with your mouse (the SheerpJ JavaScript compiler allows you to display them without a Java environment).

to live on our Earth ...

how to use LiveGraphics3D

As soon as the pointer enters an applet zone the applet takes the focus and keeps it until it leaves the zone (click outside an applet to reactivate the keyboard shortcuts).
If, to reach a pop-up window P, the pointer goes over an applet in the main window M, this applet, and thus also M, picks up again the focus and may hide P (use the task bar to give the focus back to P or minimize M).

Below "left"/"right" points out the mouse's button to click, and "Shift"/"Ctrl" points out the additional key to maintain.

drag-left to rotate the globe around its center; if the button is released while dragging the rotation continues (spin) as long as the pointer remains on the applet (it resumes when the pointer comes back on it); click again to stop the spinning
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 one by one the 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 applet; a left double click stops or restarts the animation: when stopped, drag-right horizontally controls it step by step
some graphics may be dynamically modified: if necessary stop the motion (click anywhere on the applet), then left-drag one of the big points to move it (the appearance of a little square centered on the point when the pointer hovers over it allows to identify easily such a point); click elsewhere on the applet to leave the "modify" mode
the "home" key restores the picture to its original settings

my favorite 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.
Seattle WA		An impressive collection of applets with a lot of data by David I. McCooey.
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 applet.
Zaragoza		Study of an IsoAxis object with a video clip (in Spanish, translation in French).
Brussels		The course by Xavier Hubaut: polyhedra and groups of isometries (in French).
Rennes		the nice pages by Nicolas Hannachi (Math à mâter 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 review, summarizes the many features offered by Stella, and takes stock up of the research in polyhedra theory. Stella4D by Robert Webb is the ultimate tool for 3D (polyhedra) and 4D (polytopes) investigations.

To produce the images animated with LiveGraphics3D by 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), Arnaud Chéritat (France) and Maurice Starck (New-Caledonia, France).