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#hockeypuck.g    GAP file
#
# The hockey puck puzzle is a mechanical puzzle sold at
# http://look.net/hockeypuck/
# and has a few web pages devoted to it:
# http://web.usna.navy.mil/~wdj/mball/puck.htm
# and
# http://www.geocities.com/jaapsch/puzzles/puck.htm
#
# Label the 24 pieces =1, -1, ..., +12, -12.
# The rotation r sends
# (1,-1,...,12,-12) to (12,-12,1,-1,...,11,-11).
# The flip f1 sends
# (1,-1,...,12,-12) to (-6,6,-5,5,-4,4,-3,3,-2,2,-1,1,7,-7,...,11,-11).
# The flip f2 sends
# (1,-1,...,12,-12) to (1,-1,-7,7,-6,6,...,-2,2,8,-8,...,12,-12).
# In general, (performing permutations left-to-right)
# fi=r^(i-1)*f1*r^(1-i).
#
# GAP does not allow actions on negative integers (??),
# so we write
# -1 <-> 13,
# -2 <-> 14,
# -3 <-> 15,
# -4 <-> 16,
# -5 <-> 17,
# -6 <-> 18,
# -7 <-> 19,
# -8 <-> 20,
# -9 <-> 21,
# -10 <-> 22,
# -11 <-> 23,
# -12 <-> 24.

#r:=(1,12,11,10,9,8,7,6,5,4,3,2)(-1,-12,-11,-10,-9,-8,-7,-6,-5,-4,-3,-2)
r:=(1,12,11,10,9,8,7,6,5,4,3,2)(13,24,23,22,21,20,19,18,17,16,15,14);

#f1:=(1,-6)(2,-5)(3,-4)(4,-3)(5,-2)(6,-1)
f:=[];
f[1]:=(1,18)(2,17)(3,16)(4,15)(5,14)(6,13);

for i in [2..12] do
 f[i]:=r^(i-1)*f[1]*r^(1-i);
od;

gens:=[];
Append(gens,[r]);
Append(gens,f);
puck:=Group(gens);