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Polytope of Type {6,6}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {6,6}*384c
if this polytope has a name.
Group : SmallGroup(384,17948)
Rank : 3
Schlafli Type : {6,6}
Number of vertices, edges, etc : 32, 96, 32
Order of s0s1s2 : 4
Order of s0s1s2s1 : 6
Special Properties :
   Compact Hyperbolic Quotient
   Locally Spherical
   Orientable
   Self-Dual
Related Polytopes :
   Facet
   Vertex Figure
   Dual
   Petrial
Facet Of :
   {6,6,2} of size 768
Vertex Figure Of :
   {2,6,6} of size 768
Quotients (Maximal Quotients in Boldface) :
   2-fold quotients : {6,6}*192a
   4-fold quotients : {6,6}*96
   8-fold quotients : {3,6}*48, {6,3}*48
   16-fold quotients : {3,3}*24
   48-fold quotients : {2,2}*8
Covers (Minimal Covers in Boldface) :
   2-fold covers : {6,12}*768d, {12,6}*768d, {6,6}*768b, {6,12}*768f, {12,6}*768f, {6,6}*768e, {6,12}*768i, {12,6}*768i, {6,6}*768f, {6,12}*768j, {12,6}*768j
   3-fold covers : {6,6}*1152c, {6,6}*1152d
   5-fold covers : {6,30}*1920b, {30,6}*1920b
Permutation Representation (GAP) :
s0 := ( 3, 4)( 5, 9)( 6,10)( 7,12)( 8,11)(15,16)(17,33)(18,34)(19,36)(20,35)
(21,41)(22,42)(23,44)(24,43)(25,37)(26,38)(27,40)(28,39)(29,45)(30,46)(31,48)
(32,47)(51,52)(53,57)(54,58)(55,60)(56,59)(63,64)(65,81)(66,82)(67,84)(68,83)
(69,89)(70,90)(71,92)(72,91)(73,85)(74,86)(75,88)(76,87)(77,93)(78,94)(79,96)
(80,95);;
s1 := ( 1,17)( 2,20)( 3,19)( 4,18)( 5,23)( 6,22)( 7,21)( 8,24)( 9,30)(10,31)
(11,32)(12,29)(13,28)(14,25)(15,26)(16,27)(34,36)(37,39)(41,46)(42,47)(43,48)
(44,45)(49,65)(50,68)(51,67)(52,66)(53,71)(54,70)(55,69)(56,72)(57,78)(58,79)
(59,80)(60,77)(61,76)(62,73)(63,74)(64,75)(82,84)(85,87)(89,94)(90,95)(91,96)
(92,93);;
s2 := ( 1,61)( 2,62)( 3,64)( 4,63)( 5,53)( 6,54)( 7,56)( 8,55)( 9,57)(10,58)
(11,60)(12,59)(13,49)(14,50)(15,52)(16,51)(17,93)(18,94)(19,96)(20,95)(21,85)
(22,86)(23,88)(24,87)(25,89)(26,90)(27,92)(28,91)(29,81)(30,82)(31,84)(32,83)
(33,77)(34,78)(35,80)(36,79)(37,69)(38,70)(39,72)(40,71)(41,73)(42,74)(43,76)
(44,75)(45,65)(46,66)(47,68)(48,67);;
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, s2*s0*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1, 
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 ];;
poly := F / rels;;
 
Permutation Representation (Magma) :
s0 := Sym(96)!( 3, 4)( 5, 9)( 6,10)( 7,12)( 8,11)(15,16)(17,33)(18,34)(19,36)
(20,35)(21,41)(22,42)(23,44)(24,43)(25,37)(26,38)(27,40)(28,39)(29,45)(30,46)
(31,48)(32,47)(51,52)(53,57)(54,58)(55,60)(56,59)(63,64)(65,81)(66,82)(67,84)
(68,83)(69,89)(70,90)(71,92)(72,91)(73,85)(74,86)(75,88)(76,87)(77,93)(78,94)
(79,96)(80,95);
s1 := Sym(96)!( 1,17)( 2,20)( 3,19)( 4,18)( 5,23)( 6,22)( 7,21)( 8,24)( 9,30)
(10,31)(11,32)(12,29)(13,28)(14,25)(15,26)(16,27)(34,36)(37,39)(41,46)(42,47)
(43,48)(44,45)(49,65)(50,68)(51,67)(52,66)(53,71)(54,70)(55,69)(56,72)(57,78)
(58,79)(59,80)(60,77)(61,76)(62,73)(63,74)(64,75)(82,84)(85,87)(89,94)(90,95)
(91,96)(92,93);
s2 := Sym(96)!( 1,61)( 2,62)( 3,64)( 4,63)( 5,53)( 6,54)( 7,56)( 8,55)( 9,57)
(10,58)(11,60)(12,59)(13,49)(14,50)(15,52)(16,51)(17,93)(18,94)(19,96)(20,95)
(21,85)(22,86)(23,88)(24,87)(25,89)(26,90)(27,92)(28,91)(29,81)(30,82)(31,84)
(32,83)(33,77)(34,78)(35,80)(36,79)(37,69)(38,70)(39,72)(40,71)(41,73)(42,74)
(43,76)(44,75)(45,65)(46,66)(47,68)(48,67);
poly := sub<Sym(96)|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, s2*s0*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1, 
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 >; 
 
References : None.
to this polytope