Questions?
See the FAQ
or other info.

Polytope of Type {6,6}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {6,6}*1152c
if this polytope has a name.
Group : SmallGroup(1152,155790)
Rank : 3
Schlafli Type : {6,6}
Number of vertices, edges, etc : 96, 288, 96
Order of s0s1s2 : 12
Order of s0s1s2s1 : 6
Special Properties :
   Compact Hyperbolic Quotient
   Locally Spherical
   Orientable
Related Polytopes :
   Facet
   Vertex Figure
   Dual
   Petrial
Facet Of :
   None in this Atlas
Vertex Figure Of :
   None in this Atlas
Quotients (Maximal Quotients in Boldface) :
   3-fold quotients : {6,6}*384c
   4-fold quotients : {6,6}*288a
   6-fold quotients : {6,6}*192a
   8-fold quotients : {6,3}*144
   12-fold quotients : {6,6}*96
   16-fold quotients : {6,6}*72b
   24-fold quotients : {3,6}*48, {6,3}*48
   32-fold quotients : {6,3}*36
   48-fold quotients : {3,3}*24, {2,6}*24
   96-fold quotients : {2,3}*12
   144-fold quotients : {2,2}*8
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :
s0 := ( 3, 4)( 7, 8)( 9,13)(10,14)(11,16)(12,15)(19,20)(23,24)(25,29)(26,30)
(27,32)(28,31)(35,36)(39,40)(41,45)(42,46)(43,48)(44,47);;
s1 := ( 2, 4)( 5,16)( 6,13)( 7,14)( 8,15)( 9,11)(17,33)(18,36)(19,35)(20,34)
(21,48)(22,45)(23,46)(24,47)(25,43)(26,42)(27,41)(28,44)(29,38)(30,39)(31,40)
(32,37);;
s2 := ( 1,21)( 2,22)( 3,24)( 4,23)( 5,17)( 6,18)( 7,20)( 8,19)( 9,25)(10,26)
(11,28)(12,27)(13,29)(14,30)(15,32)(16,31)(33,37)(34,38)(35,40)(36,39)(43,44)
(47,48);;
poly := Group([s0,s1,s2]);;
 
Finitely Presented Group Representation (GAP) :
F := FreeGroup("s0","s1","s2");;
s0 := F.1;;  s1 := F.2;;  s2 := F.3;;  
rels := [ s0*s0, s1*s1, s2*s2, s0*s2*s0*s2, s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1, 
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2, 
s2*s0*s1*s0*s1*s2*s0*s1*s0*s1*s2*s0*s1*s0*s1*s2*s0*s1*s0*s1, 
s2*s0*s1*s2*s1*s2*s0*s1*s0*s1*s2*s0*s1*s2*s1*s2*s0*s1*s0*s1, 
s0*s1*s2*s1*s2*s1*s0*s1*s2*s1*s0*s1*s0*s1*s2*s1*s2*s1*s0*s1*s2*s1*s0*s1 ];;
poly := F / rels;;
 
Permutation Representation (Magma) :
s0 := Sym(48)!( 3, 4)( 7, 8)( 9,13)(10,14)(11,16)(12,15)(19,20)(23,24)(25,29)
(26,30)(27,32)(28,31)(35,36)(39,40)(41,45)(42,46)(43,48)(44,47);
s1 := Sym(48)!( 2, 4)( 5,16)( 6,13)( 7,14)( 8,15)( 9,11)(17,33)(18,36)(19,35)
(20,34)(21,48)(22,45)(23,46)(24,47)(25,43)(26,42)(27,41)(28,44)(29,38)(30,39)
(31,40)(32,37);
s2 := Sym(48)!( 1,21)( 2,22)( 3,24)( 4,23)( 5,17)( 6,18)( 7,20)( 8,19)( 9,25)
(10,26)(11,28)(12,27)(13,29)(14,30)(15,32)(16,31)(33,37)(34,38)(35,40)(36,39)
(43,44)(47,48);
poly := sub<Sym(48)|s0,s1,s2>;
 
Finitely Presented Group Representation (Magma) :
poly<s0,s1,s2> := Group< s0,s1,s2 | s0*s0, s1*s1, s2*s2, 
s0*s2*s0*s2, s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1, 
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2, 
s2*s0*s1*s0*s1*s2*s0*s1*s0*s1*s2*s0*s1*s0*s1*s2*s0*s1*s0*s1, 
s2*s0*s1*s2*s1*s2*s0*s1*s0*s1*s2*s0*s1*s2*s1*s2*s0*s1*s0*s1, 
s0*s1*s2*s1*s2*s1*s0*s1*s2*s1*s0*s1*s0*s1*s2*s1*s2*s1*s0*s1*s2*s1*s0*s1 >; 
 
References : None.
to this polytope