%%%% dodec_02.ldf
%%%% Created by Laurence D. Finston (LDF) Tue Oct 16 22:49:15 CEST 2007


%% * (1) Copyright and License.

%%%% This file is part of GNU 3DLDF, a package for three-dimensional drawing.  
%%%% Copyright (C) 2007, 2008, 2009, 2010, 2011, 2012, 2013 The Free Software Foundation  

%%%% GNU 3DLDF is free software; you can redistribute it and/or modify 
%%%% it under the terms of the GNU General Public License as published by 
%%%% the Free Software Foundation; either version 3 of the License, or 
%%%% (at your option) any later version.  

%%%% GNU 3DLDF is distributed in the hope that it will be useful, 
%%%% but WITHOUT ANY WARRANTY; without even the implied warranty of 
%%%% MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the 
%%%% GNU General Public License for more details.  

%%%% You should have received a copy of the GNU General Public License 
%%%% along with GNU 3DLDF; if not, write to the Free Software 
%%%% Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA  02110-1301  USA 

%%%% GNU 3DLDF is a GNU package.  
%%%% It is part of the GNU Project of the  
%%%% Free Software Foundation 
%%%% and is published under the GNU General Public License. 
%%%% See the website http://www.gnu.org 
%%%% for more information.   
%%%% GNU 3DLDF is available for downloading from 
%%%% http://www.gnu.org/software/3dldf/LDF.html.

%%%% Please send bug reports to Laurence.Finston@gmx.de
%%%% The mailing list help-3dldf@gnu.org is available for people to 
%%%% ask other users for help.  
%%%% The mailing list info-3dldf@gnu.org is for sending 
%%%% announcements to users. To subscribe to these mailing lists, send an 
%%%% email with ``subscribe <email-address>'' as the subject.  

%%%% The author can be contacted at: 

%%%% Laurence D. Finston 
%%%% c/o Free Software Foundation, Inc. 
%%%% 51 Franklin St, Fifth Floor 
%%%% Boston, MA  02110-1301  
%%%% USA

%%%% Laurence.Finston@gmx.de
 


%% Run like this:

%% 3dldf dodec_02.ldf 
%% mpost dodec_02.mp 
%% tex dodec_02.txt 
%% dvips -o dodec_02.ps dodec_02.dvi

%% All on one line:
if false:
3dldf dodec_02.ldf; mpost dodec_02.mp; tex dodec_02.txt; \
dvips -o dodec_02.ps dodec_02.dvi
fi;

%% View using Ghostview like this:
%% gv dodec_02.ps &

% * (1) Beginning of 3DLDF code.

%% ** (2) draw_dodecahedron_net


input "dodec_02.lmc";


%% *** (3) Global declarations and initializations

focus f;
set f with_position (3, 2, -20) 
   with_direction (3, 2, 10) with_distance 20; 

polyhedron d[];

point p[];
point n[];  %% normals
point c[];  %% centers
reg_polygon r[];

string s;

%% *** (3) Figure 1

beginfig(1); 

%% !!TODO:  Find out why I couldn't make `path_pen' and `dot_pen' as typed
%%          arguments!
%%          LDF 2007.10.16.

draw_dodecahedron_net {4, true, 6, .375mm, .75mm, identity};

endfig with_projection parallel_x_z no_sort; 

%% *** (3) Figure 2

beginfig(2);
d0 := unit_dodecahedron scaled 2 rotated (180, 190);
draw d0;


for i = 0 upto 11:
   r[i] := get_reg_polygon (i) d0;
   c[i] := get_center r[i];
   if false: 
      s := decimal i;
      label(s, c[i]);
   fi; 
endfor;

if false:  
   for i = 0 upto 4:
      s := "$2_" & decimal i & "$";
      label.top(s, get_point (i) r2);
   endfor;

   for i = 0 upto 4:
      s := "$9_" & decimal i & "$";
      label.lft(s, get_point (i) r9);
   endfor;

   for i = 0 upto 4:
      s := "$10_" & decimal i & "$";
      label.rt(s, get_point (i) r10);
   endfor;
fi; 

label(1, c1);
label(2, c2);
label(9, c9);
label(11, c11);

label(10, c10);
%label(2, c2) with_text_color red;
%label.bot(1, c1) with_text_color blue;

% filldraw r1 with_draw_color blue;
% filldraw r2;
% filldraw r0;
% filldraw r6;

filldraw r1;
filldraw r2;
filldraw r9;
filldraw r10;
filldraw r11;


% filldraw r10;
% filldraw r11;


n1 := ((get_normal r1) * -1) shifted c1;

%label.urt("$n_1$", n1) with_text_color blue;
%drawarrow c1 -- n1 with_color blue;

endfig with_focus f no_sort;  

%% *** (3) Figure 3

beginfig(3);
d0 := unit_dodecahedron scaled 2 rotated (180, 10);
draw d0;

for i = 0 upto 11:
   r[i] := get_reg_polygon (i) d0;
   c[i] := get_center r[i];
   if false: 
      s := decimal i;
      label(s, c[i]);
   fi; 
endfor;

filldraw r3;
filldraw r4;
filldraw r5;
filldraw r7;
filldraw r8;

% draw r0;
% draw r1;
% draw r2;
% draw r3;
% draw r5;
% draw r6;
% draw r7;
% draw r8;
% draw r9;
% draw r10;
% draw r11;



label(3, c3);
label(4, c4);
label(5, c5);
label(7, c7);
label(8, c8);

endfig with_focus f no_sort;   


%% *** (3) Figure 4

beginfig(4); 

transform t[];
t0 := identity rotated (0, 0, -90);

draw_dodecahedron_net {6, true, 6, .4mm, .75mm, t0};

rotate current_picture (0, -75);

endfig with_projection parallel_x_z no_sort; 

%% *** (3) Figure 5.  Pentagons for cutting out, 4cm.

%% **** (4) Declarations

path q[];


%% **** (4) Figure 5

beginfig(5); 

%% ***** (5) First pentagon, r0

r0 := unit_pentagon scaled 2;

c0 := get_center r0;

%label("$r_0$", c0);

draw r0;

for i = 0 upto 4:
   p[i] := get_point (i) r0;
endfor;

%dotlabel.top("$p_0$", p0);
%dotlabel.top("$p_1$", p1);
%dotlabel.top("$p_2$", p2);
%dotlabel.top("$p_3$", p3);
%dotlabel.top("$p_4$", p4);

j := 0;
for i = 0 upto 3:
   q[i] += --;
   p[10 + j] := unit_vector (p[i] - p[i + 1]) shifted p[i];
   q[i] += p[10 + j];
   j += 1;
   p[10 + j] := unit_vector (p[i + 1] - p[i]) shifted p[i + 1];
   q[i] += p[10 + j];
   j += 1;
endfor;

p[18] := unit_vector (p[4] - p[0]) shifted p[4];
p[19] := unit_vector (p[0] - p[4]) shifted p[0];

q[4] := p[18] -- p[19];

%dotlabel.top("$p_{10}$", p10);
%dotlabel.top("$p_{11}$", p11);
%dotlabel.top("$p_{12}$", p12);
%dotlabel.top("$p_{13}$", p13);
%dotlabel.top("$p_{14}$", p14);
%dotlabel.top("$p_{15}$", p15);
%dotlabel.top("$p_{16}$", p16);
%dotlabel.top("$p_{17}$", p17);
%dotlabel.top("$p_{18}$", p18);
%dotlabel.top("$p_{19}$", p19);

for i := 0 upto 4:
   draw q[i] dashed evenly;
endfor;

%% ***** (5) Second pentagon, r1

t0 := identity shifted by (p15 - p14);

r1 := r0 transformed t0;

draw r1;

c1 := get_center r1;
%
%label("$r_1$", c1);

for i = 0 upto 4:
   p[20 + i] := get_point (i) r1;
   q[20 + i] := q[i] transformed t0;
   draw q[20 + i] dashed evenly; 
endfor;

for i = 0 upto 9:
   p[30 + i] := p[10 + i] transformed t0;
endfor;


%dotlabel.bot("$p_{20}$", p20);
%dotlabel.bot("$p_{21}$", p21);
%dotlabel.bot("$p_{22}$", p22);
%dotlabel.bot("$p_{23}$", p23);
%dotlabel.bot("$p_{24}$", p24);

%dotlabel.bot("$p_{30}$", p30);
%dotlabel.bot("$p_{31}$", p31);
%dotlabel.bot("$p_{32}$", p32);
%dotlabel.bot("$p_{33}$", p33);
%dotlabel.bot("$p_{34}$", p34);
%dotlabel.bot("$p_{35}$", p35);
%dotlabel.bot("$p_{36}$", p36);
%dotlabel.bot("$p_{37}$", p37);
%dotlabel.bot("$p_{38}$", p38);
%dotlabel.bot("$p_{39}$", p39);

%% ***** (5) Third pentagon, r2

r2 := r1 transformed t0;

c2 := get_center r2;
%
%label("$r_2$", c2);

draw r2;

for i = 0 upto 4:
   p[40 + i] := get_point (i) r2;
   q[40 + i] := q[i + 20] transformed t0;
   draw q[40 + i] dashed evenly; 
endfor;

for i = 0 upto 9:
   p[50 + i] := p[30 + i] transformed t0;
endfor;

%dotlabel.bot("$p_{40}$", p40);
%dotlabel.bot("$p_{41}$", p41);
%dotlabel.bot("$p_{42}$", p42);
%dotlabel.bot("$p_{43}$", p43);
%dotlabel.bot("$p_{44}$", p44);

%dotlabel.bot("$p_{50}$", p50);
%dotlabel.bot("$p_{51}$", p51);
%dotlabel.bot("$p_{52}$", p52);
%dotlabel.bot("$p_{53}$", p53);
%dotlabel.bot("$p_{54}$", p54);
%dotlabel.bot("$p_{55}$", p55);
%dotlabel.bot("$p_{56}$", p56);
%dotlabel.bot("$p_{57}$", p57);
%dotlabel.bot("$p_{58}$", p58);
%dotlabel.bot("$p_{59}$", p59);

%% ***** (5) Fourth pentagon, r3

r3 := r2 transformed t0;

c3 := get_center r3;
%
%label("$r_3$", c3);

draw r3;

for i = 0 upto 4:
   p[60 + i] := get_point (i) r3;
   q[60 + i] := q[i + 40] transformed t0;
   draw q[60 + i] dashed evenly; 
endfor;

for i = 0 upto 9:
   p[70 + i] := p[50 + i] transformed t0;
endfor;

%dotlabel.bot("$p_{60}$", p60);
%dotlabel.bot("$p_{61}$", p61);
%dotlabel.bot("$p_{62}$", p62);
%dotlabel.bot("$p_{63}$", p63);
%dotlabel.bot("$p_{64}$", p64);

%dotlabel.bot("$p_{70}$", p70);
%dotlabel.bot("$p_{71}$", p71);
%dotlabel.bot("$p_{72}$", p72);
%dotlabel.bot("$p_{73}$", p73);
%dotlabel.bot("$p_{74}$", p74);
%dotlabel.bot("$p_{75}$", p75);
%dotlabel.bot("$p_{76}$", p76);
%dotlabel.bot("$p_{77}$", p77);
%dotlabel.bot("$p_{78}$", p78);
%dotlabel.bot("$p_{79}$", p79);

%for i = 0 upto 3:
%   filldraw r[i];
%endfor;

%% ***** (5) Second row 

t0 := identity shifted by (p16 - p17);

for i = 0 upto 3:
   c[i] *= r[i] *= t0;
   s := "$r_{" & decimal i & "}$";
   draw r[i];
  % label(s, c[i]);
endfor;

for i = 0 upto 4:
   q[i] *= q[20 + i] *= q[40 + i] *= q[60 + i] *= t0;
   draw q[i] dashed evenly;
   draw q[20 + i] dashed evenly;
   draw q[40 + i] dashed evenly;
   draw q[60 + i] dashed evenly;
endfor;

%% ***** (5) Third row

t1 := identity shifted by (p13 - p12);

for i = 0 upto 3:
   s := "$r_{" & decimal i & "}$";
   c[i] *= r[i] *= t1;
   draw r[i];
  % label(s, c[i]);
endfor;

for i = 0 upto 4:
   q[i] *= q[20 + i] *= q[40 + i] *= q[60 + i] *= t1;
   draw q[i] dashed evenly;
   draw q[20 + i] dashed evenly;
   draw q[40 + i] dashed evenly;
   draw q[60 + i] dashed evenly;
  % label(s, c[i]);
endfor;

%% ***** (5) Fourth row 

for i = 0 upto 3:
   s := "$r_{" & decimal i & "}$";
   c[i] *= r[i] *= t0;
   draw r[i];
  % label(s, c[i]);
endfor;

for i = 0 upto 4:
   q[i] *= q[20 + i] *= q[40 + i] *= q[60 + i] *= t0;
   draw q[i] dashed evenly;
   draw q[20 + i] dashed evenly;
   draw q[40 + i] dashed evenly;
   draw q[60 + i] dashed evenly;
endfor;


%% ***** (5) Fifth row

for i = 0 upto 3:
   s := "$r_{" & decimal i & "}$";
   c[i] *= r[i] *= t1;
   draw r[i];
  % label(s, c[i]);
endfor;

for i = 0 upto 4:
   q[i] *= q[20 + i] *= q[40 + i] *= q[60 + i] *= t1;
   draw q[i] dashed evenly;
   draw q[20 + i] dashed evenly;
   draw q[40 + i] dashed evenly;
   draw q[60 + i] dashed evenly;
endfor;

%% ***** (5) Sixth row 

for i = 0 upto 3:
   s := "$r_{" & decimal i & "}$";
   c[i] *= r[i] *= t0;
   draw r[i];
  % label(s, c[i]);
endfor;

for i = 0 upto 4:
   q[i] *= q[20 + i] *= q[40 + i] *= q[60 + i] *= t0;
   draw q[i] dashed evenly;
   draw q[20 + i] dashed evenly;
   draw q[40 + i] dashed evenly;
   draw q[60 + i] dashed evenly;
endfor;

%% ***** (5) End of figure 5

endfig with_projection parallel_x_z no_sort; 


%% *** (3) Figure 6

beginfig(6); 

%% ***** (5) First pentagon, r0

r0 := unit_pentagon scaled 3;
draw r0;

c0 := get_center r0;
%
%label("$r_0$", c0);

for i = 0 upto 4:
   p[i] := get_point (i) r0;
endfor;

%dotlabel.top("$p_0$", p0);
%dotlabel.top("$p_1$", p1);
%dotlabel.top("$p_2$", p2);
%dotlabel.top("$p_3$", p3);
%dotlabel.top("$p_4$", p4);

j := 0;
for i = 0 upto 3:
   q[i] := null_path;
   q[i] += --;
   p[10 + j] := unit_vector (p[i] - p[i + 1]) shifted p[i];
   q[i] += p[10 + j];
   j += 1;
   p[10 + j] := unit_vector (p[i + 1] - p[i]) shifted p[i + 1];
   q[i] += p[10 + j];
   j += 1;
   draw q[i] dashed evenly;
endfor;

p[18] := unit_vector (p[4] - p[0]) shifted p[4];
p[19] := unit_vector (p[0] - p[4]) shifted p[0];

q[4] := p[18] -- p[19];
draw q[4] dashed evenly;

%dotlabel.top("$p_{10}$", p10);
%dotlabel.top("$p_{11}$", p11);
%dotlabel.top("$p_{12}$", p12);
%dotlabel.top("$p_{13}$", p13);
%dotlabel.top("$p_{14}$", p14);
%dotlabel.top("$p_{15}$", p15);
%dotlabel.top("$p_{16}$", p16);
%dotlabel.top("$p_{17}$", p17);
%dotlabel.top("$p_{18}$", p18);
%dotlabel.top("$p_{19}$", p19);


%% ***** (5) Second pentagon, r1

p100 := p15 shifted 1;

t0 := identity shifted by (p100 - p14);

r1 := r0 transformed t0;

c1 := get_center r1;
%
%label("$r_1$", c1);

draw r1;

for i = 0 upto 4:
   p[20 + i] := get_point (i) r1;
   q[20 + i] := q[i] transformed t0;
   draw q[20 + i] dashed evenly; 
endfor;

for i = 0 upto 9:
   p[30 + i] := p[10 + i] transformed t0;
endfor;


%dotlabel.bot("$p_{20}$", p20);
%dotlabel.bot("$p_{21}$", p21);
%dotlabel.bot("$p_{22}$", p22);
%dotlabel.bot("$p_{23}$", p23);
%dotlabel.bot("$p_{24}$", p24);

%dotlabel.bot("$p_{30}$", p30);
%dotlabel.bot("$p_{31}$", p31);
%dotlabel.bot("$p_{32}$", p32);
%dotlabel.bot("$p_{33}$", p33);
%dotlabel.bot("$p_{34}$", p34);
%dotlabel.bot("$p_{35}$", p35);
%dotlabel.bot("$p_{36}$", p36);
%dotlabel.bot("$p_{37}$", p37);
%dotlabel.bot("$p_{38}$", p38);
%dotlabel.bot("$p_{39}$", p39);

%% ***** (5) Third pentagon, r2

r2 := r1 transformed t0;

c2 := get_center r2;
%
%label("$r_2$", c2);

draw r2;

for i = 0 upto 4:
   p[40 + i] := get_point (i) r2;
   q[40 + i] := q[i + 20] transformed t0;
   draw q[40 + i] dashed evenly; 
endfor;

for i = 0 upto 9:
   p[50 + i] := p[30 + i] transformed t0;
endfor;

%dotlabel.bot("$p_{40}$", p40);
%dotlabel.bot("$p_{41}$", p41);
%dotlabel.bot("$p_{42}$", p42);
%dotlabel.bot("$p_{43}$", p43);
%dotlabel.bot("$p_{44}$", p44);

%dotlabel.bot("$p_{50}$", p50);
%dotlabel.bot("$p_{51}$", p51);
%dotlabel.bot("$p_{52}$", p52);
%dotlabel.bot("$p_{53}$", p53);
%dotlabel.bot("$p_{54}$", p54);
%dotlabel.bot("$p_{55}$", p55);
%dotlabel.bot("$p_{56}$", p56);
%dotlabel.bot("$p_{57}$", p57);
%dotlabel.bot("$p_{58}$", p58);
%dotlabel.bot("$p_{59}$", p59);


%% ***** (5) Second row 

t0 := identity shifted (0, 0, -6);

for i = 0 upto 2:
   s := "$r_{" & decimal i & "}$";
   c[i] *= r[i] *= t0;
   draw r[i];
  % label(s, c[i]);
endfor;

for i = 0 upto 4:
  q[i] *= q[20 + i] *= q[40 + i] *= q[60 + i] *= t0;
  draw q[i] dashed evenly;
  draw q[20 + i] dashed evenly;
  draw q[40 + i] dashed evenly;
  draw q[60 + i] dashed evenly;
endfor;
 

%% ***** (5) Third row 

for i = 0 upto 2:
   s := "$r_{" & decimal i & "}$";
   c[i] *= r[i] *= t0;
   draw r[i];
  % label(s, c[i]);
endfor;

for i = 0 upto 4:
  q[i] *= q[20 + i] *= q[40 + i] *= q[60 + i] *= t0;
  draw q[i] dashed evenly;
  draw q[20 + i] dashed evenly;
  draw q[40 + i] dashed evenly;
  draw q[60 + i] dashed evenly;
endfor;


%% ***** (5) Fourth row 

for i = 0 upto 2:
   s := "$r_{" & decimal i & "}$";
   c[i] *= r[i] *= t0;
   draw r[i];
  % label(s, c[i]);
endfor;

for i = 0 upto 4:
  q[i] *= q[20 + i] *= q[40 + i] *= q[60 + i] *= t0;
  draw q[i] dashed evenly;
  draw q[20 + i] dashed evenly;
  draw q[40 + i] dashed evenly;
  draw q[60 + i] dashed evenly;
endfor;

%% ***** (5) End of figure 6

endfig with_projection parallel_x_z no_sort; 

%% **** (4) 

%% *** (3) End of 3DLDF code

verbatim_metapost "end;";

end;

%% ** (2) 

%% * (1) Emacs-Lisp code for use in indirect buffers when using the          
%%   	 GNU Emacs editor.  The local variable list is not evaluated when an 
%%   	 indirect buffer is visited, so it's necessary to evaluate the       
%%   	 following s-expression in order to use the facilities normally      
%%   	 accessed via the local variables list.                              
%%   	 \initials{LDF 2004.02.12}.                                          

%% (progn (metafont-mode) (outline-minor-mode t) (setq fill-column 80))    

%% * (1) Local variables for Emacs.

%% Local Variables:
%% mode:Metafont
%% eval:(outline-minor-mode t)
%% eval:(read-abbrev-file abbrev-file-name)
%% outline-regexp:"%% [*\f]+"
%% End: