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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] [-delay usecs] [-fps] [-5-cell] [-8-cell]  [-16-cell]
       [-24-cell]  [-120-cell] [-600-cell] [-wireframe] [-surface] [-transpar‐
       ent]   [-single-color]	[-depth-colors]	  [-perspective-3d]   [-ortho‐
       graphic-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.

       -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 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-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, mod‐
       ify, distribute, and sell this software and its documentation  for  any
       purpose	is  hereby  granted without fee, provided that the above copy‐
       right notice appear in all copies and that both that  copyright	notice
       and this permission notice appear in supporting documentation.  No rep‐
       resentations 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		      5.07 (10-Aug-2008)		  polytopes(6)
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