Polytope of Type {2,6,12,2}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,6,12,2}*1152b
if this polytope has a name.
Group : SmallGroup(1152,157863)
Rank : 5
Schlafli Type : {2,6,12,2}
Number of vertices, edges, etc : 2, 12, 72, 24, 2
Order of s₀s₁s₂s₃s₄ : 6
Order of s₀s₁s₂s₃s₄s₃s₂s₁ : 2
Special Properties :
   Degenerate
   Universal
   Orientable
   Flat
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   None in this Atlas
Vertex Figure Of :
   None in this Atlas
Quotients (Maximal Quotients in Boldface) :
   2-fold quotients : {2,3,12,2}*576
   3-fold quotients : {2,6,4,2}*384
   4-fold quotients : {2,6,6,2}*288c
   6-fold quotients : {2,3,4,2}*192, {2,6,4,2}*192b, {2,6,4,2}*192c
   8-fold quotients : {2,3,6,2}*144
   12-fold quotients : {2,3,4,2}*96, {2,6,2,2}*96
   24-fold quotients : {2,3,2,2}*48
   36-fold quotients : {2,2,2,2}*32
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :

s0 := (1,2);;
s1 := ( 4, 5)( 7,11)( 8,13)( 9,12)(10,14)(15,27)(16,29)(17,28)(18,30)(19,35)
(20,37)(21,36)(22,38)(23,31)(24,33)(25,32)(26,34)(40,41)(43,47)(44,49)(45,48)
(46,50)(51,63)(52,65)(53,64)(54,66)(55,71)(56,73)(57,72)(58,74)(59,67)(60,69)
(61,68)(62,70);;
s2 := ( 3,55)( 4,56)( 5,58)( 6,57)( 7,51)( 8,52)( 9,54)(10,53)(11,59)(12,60)
(13,62)(14,61)(15,43)(16,44)(17,46)(18,45)(19,39)(20,40)(21,42)(22,41)(23,47)
(24,48)(25,50)(26,49)(27,67)(28,68)(29,70)(30,69)(31,63)(32,64)(33,66)(34,65)
(35,71)(36,72)(37,74)(38,73);;
s3 := ( 3, 6)( 4, 5)( 7,14)( 8,13)( 9,12)(10,11)(15,18)(16,17)(19,26)(20,25)
(21,24)(22,23)(27,30)(28,29)(31,38)(32,37)(33,36)(34,35)(39,42)(40,41)(43,50)
(44,49)(45,48)(46,47)(51,54)(52,53)(55,62)(56,61)(57,60)(58,59)(63,66)(64,65)
(67,74)(68,73)(69,72)(70,71);;
s4 := (75,76);;
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, s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2, 
s1*s2*s3*s2*s1*s2*s1*s2*s3*s2*s1*s2, 
s3*s1*s2*s3*s1*s2*s3*s1*s2*s3*s1*s2*s3*s1*s2*s3*s1*s2, 
s3*s1*s2*s3*s2*s3*s2*s3*s2*s3*s1*s2*s3*s2*s3*s2*s3*s2 ];;
poly := F / rels;;

Permutation Representation (Magma) :

s0 := Sym(76)!(1,2);
s1 := Sym(76)!( 4, 5)( 7,11)( 8,13)( 9,12)(10,14)(15,27)(16,29)(17,28)(18,30)
(19,35)(20,37)(21,36)(22,38)(23,31)(24,33)(25,32)(26,34)(40,41)(43,47)(44,49)
(45,48)(46,50)(51,63)(52,65)(53,64)(54,66)(55,71)(56,73)(57,72)(58,74)(59,67)
(60,69)(61,68)(62,70);
s2 := Sym(76)!( 3,55)( 4,56)( 5,58)( 6,57)( 7,51)( 8,52)( 9,54)(10,53)(11,59)
(12,60)(13,62)(14,61)(15,43)(16,44)(17,46)(18,45)(19,39)(20,40)(21,42)(22,41)
(23,47)(24,48)(25,50)(26,49)(27,67)(28,68)(29,70)(30,69)(31,63)(32,64)(33,66)
(34,65)(35,71)(36,72)(37,74)(38,73);
s3 := Sym(76)!( 3, 6)( 4, 5)( 7,14)( 8,13)( 9,12)(10,11)(15,18)(16,17)(19,26)
(20,25)(21,24)(22,23)(27,30)(28,29)(31,38)(32,37)(33,36)(34,35)(39,42)(40,41)
(43,50)(44,49)(45,48)(46,47)(51,54)(52,53)(55,62)(56,61)(57,60)(58,59)(63,66)
(64,65)(67,74)(68,73)(69,72)(70,71);
s4 := Sym(76)!(75,76);
poly := sub<Sym(76)|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, 
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2, 
s1*s2*s3*s2*s1*s2*s1*s2*s3*s2*s1*s2, 
s3*s1*s2*s3*s1*s2*s3*s1*s2*s3*s1*s2*s3*s1*s2*s3*s1*s2, 
s3*s1*s2*s3*s2*s3*s2*s3*s2*s3*s1*s2*s3*s2*s3*s2*s3*s2 >;

to this polytope