Provided by: xscreensaver-gl_5.36-1ubuntu1_amd64 
NAME
polytopes - Draws one of the six regular 4d polytopes rotating in 4d.
SYNOPSIS
polytopes [-display host:display.screen] [-install] [-visual visual] [-window] [-root] [-delay usecs]
[-fps] [-5-cell] [-8-cell] [-16-cell] [-24-cell] [-120-cell] [-600-cell] [-wireframe] [-surface]
[-transparent] [-single-color] [-depth-colors] [-perspective-3d] [-orthographic-3d] [-perspective-4d]
[-orthographic-4d] [-speed-wx float] [-speed-wy float] [-speed-wz float] [-speed-xy float] [-speed-xz
float] [-speed-yz float]
DESCRIPTION
The polytopes program shows one of the six regular 4d polytopes (5-cell, 8-cell, 16-cell, 24-cell,
120-cell, or 600-cell) rotating in 4d. The program projects the 4d polytope to 3d using either a
perspective or an orthographic projection. The projected 3d polytope can then be projected to the screen
either perspectively or orthographically. There are three display modes for the polytope: mesh
(wireframe), solid, or transparent. Furthermore, the colors with which the polytope is drawn can be set
to either single color or to a coloring according to the 4d "depth" (the w coordinate) of the polytope in
its unrotated position. In the first case, the polytope is drawn in red. This coloring combined with
transparency gives a nice visual effect of the structure of the polytope. The second mode draws the
polytope with a fully saturated color wheel in which the edges or faces are colored accoring to their
average 4d "depth". This mode is best combined with the wireframe mode, where it allows you to see how
different parts of the polytope are moved to the "inside" of the projected polytope in 3d. Of course, in
4d the cells, faces, and edges of the polytope all have the same distance from the center of the
polytope. Only the projection creates the appearance that some of the cells lie "inside" the figure in
3d.
OPTIONS
polytopes accepts the following options:
-window Draw on a newly-created window. This is the default.
-root Draw on the root window.
-install
Install a private colormap for the window.
-visual visual
Specify which visual to use. Legal values are the name of a visual class, or the id number
(decimal or hex) of a specific visual.
-delay microseconds
How much of a delay should be introduced between steps of the animation. Default 25000, or
1/40th second.
The following six options are mutually exclusive. They determine which polytope is displayed.
-5-cell Display the 5-cell. The 5-cell is the 4d analogon of a regular tetrahedron in 3d. It has 5
regular tetrahedra as its cells, 10 equilateral triangles as faces, 10 edges, and 5 vertices.
-8-cell Display the 8-cell (a.k.a. hypercube or tessaract). The 8-cell is the 4d analogon of a cube in
3d. It has 8 cubes as its cells, 24 squares as faces, 32 edges, and 16 vertices.
-16-cell
Display the 16-cell. The 16-cell is the 4d analogon of an octahedron in 3d. It has 16 regular
tetrahedra as its cells, 32 equilateral triangles as faces, 24 edges, and 8 vertices.
-24-cell
Display the 24-cell. The 24-cell has no 3d analogon. It has 24 regular octahedra as its cells,
96 equilateral triangles as faces, 96 edges, and 24 vertices.
-120-cell
Display the 120-cell. The 120-cell has no 3d analogon. It has 120 regular dodecahedra as its
cells, 720 regular pentagons as faces, 1200 edges, and 600 vertices.
-600-cell
Display the 600-cell. The 600-cell has no 3d analogon. It has 600 regular tetrahedra as its
cells, 1200 equilateral triangles as faces, 720 edges, and 120 vertices.
The following three options are mutually exclusive. They determine how the polytope is displayed.
-wireframe
Display the polytope as a wireframe mesh.
-surface
Display the polytope as a solid object.
-transparent
Display the polytope as a transparent object (default).
The following two options are mutually exclusive. They determine how to color the polytope.
-single-color
Display the polytope in red.
-depth-colors
Display the polytope with a fully saturated color wheel in which the edges or faces are colored
accoring to their average 4d "depth", i.e., the w coordinate of the polytope in its unrotated
position (default).
The following two options are mutually exclusive. They determine how the polytope is projected from 3d
to 2d (i.e., to the screen).
-perspective-3d
Project the polytope from 3d to 2d using a perspective projection (default).
-orthographic-3d
Project the polytope from 3d to 2d using an orthographic projection.
The following two options are mutually exclusive. They determine how the polytope is projected from 4d
to 3d.
-perspective-4d
Project the polytope from 4d to 3d using a perspective projection (default).
-orthographic-4d
Project the polytope from 4d to 3d using an orthographic projection.
The following six options determine the rotation speed of the polytope around the six possible
hyperplanes. The rotation speed is measured in degrees per frame. The speeds should be set to
relatively small values, e.g., less than 4 in magnitude.
-speed-wx float
Rotation speed around the wx plane (default: 1.1).
-speed-wy float
Rotation speed around the wy plane (default: 1.3).
-speed-wz float
Rotation speed around the wz plane (default: 1.5).
-speed-xy float
Rotation speed around the xy plane (default: 1.7).
-speed-xz float
Rotation speed around the xz plane (default: 1.9).
-speed-yz float
Rotation speed around the yz plane (default: 2.1).
INTERACTION
If you run this program in standalone mode you can rotate the polytope by dragging the mouse while
pressing the left mouse button. This rotates the polytope in 3D, i.e., around the wx, wy, and wz planes.
If you press the shift key while dragging the mouse with the left button pressed the polytope is rotated
in 4D, i.e., around the xy, xz, and yz planes. To examine the polytope at your leisure, it is best to
set all speeds to 0. Otherwise, the polytope will rotate while the left mouse button is not pressed.
-fps Display the current frame rate, CPU load, and polygon count.
ENVIRONMENT
DISPLAY to get the default host and display number.
XENVIRONMENT
to get the name of a resource file that overrides the global resources stored in the
RESOURCE_MANAGER property.
SEE ALSO
X(1), xscreensaver(1)
COPYRIGHT
Copyright © 2003-2005 by Carsten Steger. Permission to use, copy, modify, distribute, and sell this
software and its documentation for any purpose is hereby granted without fee, provided that the above
copyright notice appear in all copies and that both that copyright notice and this permission notice
appear in supporting documentation. No representations are made about the suitability of this software
for any purpose. It is provided "as is" without express or implied warranty.
AUTHOR
Carsten Steger <carsten@mirsanmir.org>, 28-sep-2005.