polytopes(6) XScreenSaver manual polytopes(6)

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 (C) 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.

X Version 11 6.09 (07-Jun-2024) polytopes(6)