Provided by: xscreensaver-gl_6.08+dfsg1-1ubuntu3_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] [--window-id number] [--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 according 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.
--window-id number
Draw on the specified 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 according 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.
XSCREENSAVER_WINDOW
The window ID to use with --root.
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.