Polytope of Type {2,2,24,6}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,2,24,6}*1152c
if this polytope has a name.
Group : SmallGroup(1152,152551)
Rank : 5
Schlafli Type : {2,2,24,6}
Number of vertices, edges, etc : 2, 2, 24, 72, 6
Order of s₀s₁s₂s₃s₄ : 24
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 : {2,2,12,6}*576b
   3-fold quotients : {2,2,24,2}*384
   4-fold quotients : {2,2,6,6}*288c
   6-fold quotients : {2,2,12,2}*192
   8-fold quotients : {2,2,3,6}*144
   9-fold quotients : {2,2,8,2}*128
   12-fold quotients : {2,2,6,2}*96
   18-fold quotients : {2,2,4,2}*64
   24-fold quotients : {2,2,3,2}*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 := (3,4);;
s2 := ( 6, 7)( 8,11)( 9,13)(10,12)(15,16)(17,20)(18,22)(19,21)(23,32)(24,34)
(25,33)(26,38)(27,40)(28,39)(29,35)(30,37)(31,36)(41,59)(42,61)(43,60)(44,65)
(45,67)(46,66)(47,62)(48,64)(49,63)(50,68)(51,70)(52,69)(53,74)(54,76)(55,75)
(56,71)(57,73)(58,72);;
s3 := ( 5,45)( 6,44)( 7,46)( 8,42)( 9,41)(10,43)(11,48)(12,47)(13,49)(14,54)
(15,53)(16,55)(17,51)(18,50)(19,52)(20,57)(21,56)(22,58)(23,72)(24,71)(25,73)
(26,69)(27,68)(28,70)(29,75)(30,74)(31,76)(32,63)(33,62)(34,64)(35,60)(36,59)
(37,61)(38,66)(39,65)(40,67);;
s4 := ( 6, 7)( 9,10)(12,13)(15,16)(18,19)(21,22)(24,25)(27,28)(30,31)(33,34)
(36,37)(39,40)(42,43)(45,46)(48,49)(51,52)(54,55)(57,58)(60,61)(63,64)(66,67)
(69,70)(72,73)(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, s1*s2*s1*s2, s0*s3*s0*s3, 
s1*s3*s1*s3, s0*s4*s0*s4, s1*s4*s1*s4, 
s2*s4*s2*s4, s4*s2*s3*s4*s3*s4*s2*s3*s4*s3, 
s2*s3*s4*s3*s2*s3*s2*s3*s4*s3*s2*s3, 
s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3 ];;
poly := F / rels;;

Permutation Representation (Magma) :

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

to this polytope