xscreensaver(1)

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]  [-mesh]  [-surface]  [-transparent] [-singlecolor]    [-depth-colors]    [-perspective-3d]    [-ortho
graphic-3d]  [-perspective-4d] [-orthographic-4d] [-speedwx 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 ortho
graphic projection. The projected 3d polytope can then be
projected to the screen either perspectively or ortho
graphically. There are three display modes for the poly
tope: mesh (wireframe), solid, or transparent. Further
more, 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 poly
tope. The second mode draws the polytope with a fully
saturated color wheel in which the edges or faces are col
ored 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 tessar

act). 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 analo
gon 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 analo
gon. 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.

-mesh Display the polytope as a wireframe mesh

(default).

-surface

Display the polytope as a solid object.

-transparent

Display the polytope as a transparent object.

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 posi
tion (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 per
spective projection (default).

-orthographic-3d

Project the polytope from 3d to 2d using an ortho
graphic 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 per
spective projection (default).

-orthographic-4d

Project the polytope from 4d to 3d using an ortho
graphic 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-xw float

Rotation speed around the wx plane (default: 1.1).

-speed-xy 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).

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_MAN
AGER property.

SEE ALSO

X(1), xscreensaver(1)

COPYRIGHT

Copyright © 2003 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>, 10-aug-2003.