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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.