Polytope of Type {2,6,6,4}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,6,6,4}*576f
if this polytope has a name.
Group : SmallGroup(576,8659)
Rank : 5
Schlafli Type : {2,6,6,4}
Number of vertices, edges, etc : 2, 6, 18, 12, 4
Order of s₀s₁s₂s₃s₄ : 6
Order of s₀s₁s₂s₃s₄s₃s₂s₁ : 2
Special Properties :
   Degenerate
   Universal
   Non-Orientable
   Flat
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   {2,6,6,4,2} of size 1152
Vertex Figure Of :
   {2,2,6,6,4} of size 1152
   {3,2,6,6,4} of size 1728
Quotients (Maximal Quotients in Boldface) :
   2-fold quotients : {2,6,3,4}*288
   3-fold quotients : {2,2,6,4}*192b
   6-fold quotients : {2,2,3,4}*96
Covers (Minimal Covers in Boldface) :
   2-fold covers : {4,6,6,4}*1152h, {2,6,6,4}*1152b
   3-fold covers : {2,6,18,4}*1728e, {2,6,6,4}*1728f, {6,6,6,4}*1728l, {2,6,6,12}*1728h
Permutation Representation (GAP) :

s0 := (1,2);;
s1 := ( 7,11)( 8,12)( 9,13)(10,14)(19,23)(20,24)(21,25)(22,26)(31,35)(32,36)
(33,37)(34,38)(43,47)(44,48)(45,49)(46,50)(55,59)(56,60)(57,61)(58,62)(67,71)
(68,72)(69,73)(70,74);;
s2 := ( 3, 7)( 4, 9)( 5, 8)( 6,10)(12,13)(15,31)(16,33)(17,32)(18,34)(19,27)
(20,29)(21,28)(22,30)(23,35)(24,37)(25,36)(26,38)(39,43)(40,45)(41,44)(42,46)
(48,49)(51,67)(52,69)(53,68)(54,70)(55,63)(56,65)(57,64)(58,66)(59,71)(60,73)
(61,72)(62,74);;
s3 := ( 3,51)( 4,52)( 5,54)( 6,53)( 7,59)( 8,60)( 9,62)(10,61)(11,55)(12,56)
(13,58)(14,57)(15,39)(16,40)(17,42)(18,41)(19,47)(20,48)(21,50)(22,49)(23,43)
(24,44)(25,46)(26,45)(27,63)(28,64)(29,66)(30,65)(31,71)(32,72)(33,74)(34,73)
(35,67)(36,68)(37,70)(38,69);;
s4 := ( 3,42)( 4,41)( 5,40)( 6,39)( 7,46)( 8,45)( 9,44)(10,43)(11,50)(12,49)
(13,48)(14,47)(15,54)(16,53)(17,52)(18,51)(19,58)(20,57)(21,56)(22,55)(23,62)
(24,61)(25,60)(26,59)(27,66)(28,65)(29,64)(30,63)(31,70)(32,69)(33,68)(34,67)
(35,74)(36,73)(37,72)(38,71);;
poly := Group([s0,s1,s2,s3,s4]);;

Finitely Presented Group Representation (GAP) :

F := FreeGroup("s0","s1","s2","s3","s4");;
s0 := F.1;;  s1 := F.2;;  s2 := F.3;;  s3 := F.4;;  s4 := F.5;;  
rels := [ s0*s0, s1*s1, s2*s2, s3*s3, s4*s4, s0*s1*s0*s1, 
s0*s2*s0*s2, s0*s3*s0*s3, s1*s3*s1*s3, 
s0*s4*s0*s4, s1*s4*s1*s4, s2*s4*s2*s4, 
s3*s4*s3*s4*s3*s4*s3*s4, s2*s3*s4*s2*s3*s4*s2*s3*s4, 
s3*s1*s2*s1*s2*s3*s1*s2*s1*s2 ];;
poly := F / rels;;

Permutation Representation (Magma) :

s0 := Sym(74)!(1,2);
s1 := Sym(74)!( 7,11)( 8,12)( 9,13)(10,14)(19,23)(20,24)(21,25)(22,26)(31,35)
(32,36)(33,37)(34,38)(43,47)(44,48)(45,49)(46,50)(55,59)(56,60)(57,61)(58,62)
(67,71)(68,72)(69,73)(70,74);
s2 := Sym(74)!( 3, 7)( 4, 9)( 5, 8)( 6,10)(12,13)(15,31)(16,33)(17,32)(18,34)
(19,27)(20,29)(21,28)(22,30)(23,35)(24,37)(25,36)(26,38)(39,43)(40,45)(41,44)
(42,46)(48,49)(51,67)(52,69)(53,68)(54,70)(55,63)(56,65)(57,64)(58,66)(59,71)
(60,73)(61,72)(62,74);
s3 := Sym(74)!( 3,51)( 4,52)( 5,54)( 6,53)( 7,59)( 8,60)( 9,62)(10,61)(11,55)
(12,56)(13,58)(14,57)(15,39)(16,40)(17,42)(18,41)(19,47)(20,48)(21,50)(22,49)
(23,43)(24,44)(25,46)(26,45)(27,63)(28,64)(29,66)(30,65)(31,71)(32,72)(33,74)
(34,73)(35,67)(36,68)(37,70)(38,69);
s4 := Sym(74)!( 3,42)( 4,41)( 5,40)( 6,39)( 7,46)( 8,45)( 9,44)(10,43)(11,50)
(12,49)(13,48)(14,47)(15,54)(16,53)(17,52)(18,51)(19,58)(20,57)(21,56)(22,55)
(23,62)(24,61)(25,60)(26,59)(27,66)(28,65)(29,64)(30,63)(31,70)(32,69)(33,68)
(34,67)(35,74)(36,73)(37,72)(38,71);
poly := sub<Sym(74)|s0,s1,s2,s3,s4>;

Finitely Presented Group Representation (Magma) :

poly<s0,s1,s2,s3,s4> := Group< s0,s1,s2,s3,s4 | s0*s0, s1*s1, s2*s2, 
s3*s3, s4*s4, s0*s1*s0*s1, s0*s2*s0*s2, 
s0*s3*s0*s3, s1*s3*s1*s3, s0*s4*s0*s4, 
s1*s4*s1*s4, s2*s4*s2*s4, s3*s4*s3*s4*s3*s4*s3*s4, 
s2*s3*s4*s2*s3*s4*s2*s3*s4, s3*s1*s2*s1*s2*s3*s1*s2*s1*s2 >;

to this polytope