Provided by: xscreensaver-gl_5.04-4ubuntu1_i386 bug

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.

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.