polytopes



XScreenSaver(1)                                                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]
       [-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 perspec-
       tive 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  col-
       oring  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.

       -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 unro-
               tated 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  projec-
               tion (default).

       -orthographic-3d
               Project  the  polytope from 3d to 2d using an orthographic pro-
               jection.

       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 projec-
               tion (default).

       -orthographic-4d
               Project the polytope from 4d to 3d using an  orthographic  pro-
               jection.

       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 val-
       ues, 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_MANAGER 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  pur-
       pose  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 repre-
       sentations are made about the suitability of this software for any pur-
       pose.  It is provided "as is" without express or implied warranty.


AUTHOR

       Carsten Steger <carsten@mirsanmir.org>, 10-aug-2003.



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