\datethis
@*Intro. This program simply generates data for {\mc GDANCE} to
solve the problem of placing MacMahon's 24 triangles into a regular
hexagon, as discussed in Martin Gardner in Chapter 16 of
{\sl Mathematical Magic Show}. But instead of making the outside edge
a solid color, I'm trying for a solution with $180^\circ$ symmetry
when we map the colors $\.a\leftrightarrow\.d$, $\.b\leftrightarrow\.c$.

And it should tile the plane too.

@c
char piece[24][4]={
{'a','a','a',0},
{'d','d','d',0},
{'b','b','b',0},
{'c','c','c',0},
{'a','a','d',0},
{'d','d','a',0},
{'a','a','b',0},
{'d','d','c',0},
{'a','a','c',0},
{'d','d','b',0},
{'b','b','a',0},
{'c','c','d',0},
{'b','b','c',0},
{'c','c','b',0},
{'b','b','d',0},
{'c','c','a',0},
{'a','b','c',0},
{'b','d','c',0},
{'a','b','d',0},
{'a','d','c',0},
{'a','c','d',0},
{'a','d','b',0},
{'a','c','b',0},
{'b','c','d',0},
};
char pos[36][4]={
{2,3,8,0},
{3,0,4,0},
{4,5,9,0},
{5,1,6,0},
{6,7,10,0},
{11,12,19,0},
{12,8,13,0},
{13,14,20,0},
{14,9,15,0},
{15,16,21,0},
{16,10,17,0},
{17,18,22,0},
};
char map[23]={0,0,11,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,7,19,20,20,19};
main()
{
  register int j,k;
  for (k=12;k<36;k++)
    pos[k][0]=pos[k-12][1], pos[k][1]=pos[k-12][2], pos[k][2]=pos[k-12][0];
  @<Output the first line of dance data@>;
  for (j=0;j<24;j++)
    for (k=0;k<(j>=4?36: 12);k++)
      @<Generate rows for piece |j| in position |k|@>;
}

@ @<Generate rows for piece |j| in position |k|@>=
{
  printf("%s P%02d", piece[j],k%12);
  if (map[pos[k][0]]==pos[k][0]) printf(" %02d:%c",pos[k][0],piece[j][0]);
  else printf(" %02d:%c",map[pos[k][0]],'a'+'d'-piece[j][0]);
  if (map[pos[k][1]]==pos[k][1]) printf(" %02d:%c",pos[k][1],piece[j][1]);
  else printf(" %02d:%c",map[pos[k][1]],'a'+'d'-piece[j][1]);
  if (map[pos[k][2]]==pos[k][2]) printf(" %02d:%c",pos[k][2],piece[j][2]);
  else printf(" %02d:%c",map[pos[k][2]],'a'+'d'-piece[j][2]);
  printf(" %s\n",piece[j^1]);
}

@ @<Output the first line of dance data@>=
for (j=0;j<24;j++) printf("%s ",piece[j]);
for (k=0;k<12;k++) printf("P%02d ",k);
printf("|");
for (k=0;k<21;k++) if (k!=1 && k!=2 && k!=18) printf(" %02d",k);
printf("\n");

@*Index.