Polytope of Type {22,6}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {22,6}*264
Also Known As : {22,6|2}. if this polytope has another name.
Group : SmallGroup(264,34)
Rank : 3
Schlafli Type : {22,6}
Number of vertices, edges, etc : 22, 66, 6
Order of s₀s₁s₂ : 66
Order of s₀s₁s₂s₁ : 2
Special Properties :
   Compact Hyperbolic Quotient
   Locally Spherical
   Orientable
   Flat
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   {22,6,2} of size 528
   {22,6,3} of size 792
   {22,6,4} of size 1056
   {22,6,3} of size 1056
   {22,6,4} of size 1056
   {22,6,6} of size 1584
   {22,6,6} of size 1584
   {22,6,6} of size 1584
Vertex Figure Of :
   {2,22,6} of size 528
   {4,22,6} of size 1056
   {6,22,6} of size 1584
Quotients (Maximal Quotients in Boldface) :
   3-fold quotients : {22,2}*88
   6-fold quotients : {11,2}*44
   11-fold quotients : {2,6}*24
   22-fold quotients : {2,3}*12
   33-fold quotients : {2,2}*8
Covers (Minimal Covers in Boldface) :
   2-fold covers : {22,12}*528, {44,6}*528a
   3-fold covers : {22,18}*792, {66,6}*792a, {66,6}*792b
   4-fold covers : {22,24}*1056, {88,6}*1056, {44,12}*1056, {44,6}*1056
   5-fold covers : {22,30}*1320, {110,6}*1320
   6-fold covers : {22,36}*1584, {44,18}*1584a, {132,6}*1584a, {66,12}*1584a, {66,12}*1584b, {132,6}*1584b
   7-fold covers : {22,42}*1848, {154,6}*1848
Permutation Representation (GAP) :

s0 := ( 2,11)( 3,10)( 4, 9)( 5, 8)( 6, 7)(13,22)(14,21)(15,20)(16,19)(17,18)
(24,33)(25,32)(26,31)(27,30)(28,29)(35,44)(36,43)(37,42)(38,41)(39,40)(46,55)
(47,54)(48,53)(49,52)(50,51)(57,66)(58,65)(59,64)(60,63)(61,62);;
s1 := ( 1, 2)( 3,11)( 4,10)( 5, 9)( 6, 8)(12,24)(13,23)(14,33)(15,32)(16,31)
(17,30)(18,29)(19,28)(20,27)(21,26)(22,25)(34,35)(36,44)(37,43)(38,42)(39,41)
(45,57)(46,56)(47,66)(48,65)(49,64)(50,63)(51,62)(52,61)(53,60)(54,59)
(55,58);;
s2 := ( 1,45)( 2,46)( 3,47)( 4,48)( 5,49)( 6,50)( 7,51)( 8,52)( 9,53)(10,54)
(11,55)(12,34)(13,35)(14,36)(15,37)(16,38)(17,39)(18,40)(19,41)(20,42)(21,43)
(22,44)(23,56)(24,57)(25,58)(26,59)(27,60)(28,61)(29,62)(30,63)(31,64)(32,65)
(33,66);;
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*s2*s1*s0*s1*s2*s1, 
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2, 
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1 ];;
poly := F / rels;;

Permutation Representation (Magma) :

s0 := Sym(66)!( 2,11)( 3,10)( 4, 9)( 5, 8)( 6, 7)(13,22)(14,21)(15,20)(16,19)
(17,18)(24,33)(25,32)(26,31)(27,30)(28,29)(35,44)(36,43)(37,42)(38,41)(39,40)
(46,55)(47,54)(48,53)(49,52)(50,51)(57,66)(58,65)(59,64)(60,63)(61,62);
s1 := Sym(66)!( 1, 2)( 3,11)( 4,10)( 5, 9)( 6, 8)(12,24)(13,23)(14,33)(15,32)
(16,31)(17,30)(18,29)(19,28)(20,27)(21,26)(22,25)(34,35)(36,44)(37,43)(38,42)
(39,41)(45,57)(46,56)(47,66)(48,65)(49,64)(50,63)(51,62)(52,61)(53,60)(54,59)
(55,58);
s2 := Sym(66)!( 1,45)( 2,46)( 3,47)( 4,48)( 5,49)( 6,50)( 7,51)( 8,52)( 9,53)
(10,54)(11,55)(12,34)(13,35)(14,36)(15,37)(16,38)(17,39)(18,40)(19,41)(20,42)
(21,43)(22,44)(23,56)(24,57)(25,58)(26,59)(27,60)(28,61)(29,62)(30,63)(31,64)
(32,65)(33,66);
poly := sub<Sym(66)|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*s2*s1*s0*s1*s2*s1, 
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2, 
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1 >;

References : None.
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