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

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,2,6,24}*1152a
if this polytope has a name.
Group : SmallGroup(1152,152550)
Rank : 5
Schlafli Type : {2,2,6,24}
Number of vertices, edges, etc : 2, 2, 6, 72, 24
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 : {2,2,6,12}*576c
   3-fold quotients : {2,2,6,8}*384
   4-fold quotients : {2,2,6,6}*288c
   6-fold quotients : {2,2,6,4}*192a
   8-fold quotients : {2,2,3,6}*144
   9-fold quotients : {2,2,2,8}*128
   12-fold quotients : {2,2,6,2}*96
   18-fold quotients : {2,2,2,4}*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)(24,25)(26,29)
(27,31)(28,30)(33,34)(35,38)(36,40)(37,39)(42,43)(44,47)(45,49)(46,48)(51,52)
(53,56)(54,58)(55,57)(60,61)(62,65)(63,67)(64,66)(69,70)(71,74)(72,76)
(73,75);;
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 := ( 8,11)( 9,12)(10,13)(17,20)(18,21)(19,22)(23,32)(24,33)(25,34)(26,38)
(27,39)(28,40)(29,35)(30,36)(31,37)(41,59)(42,60)(43,61)(44,65)(45,66)(46,67)
(47,62)(48,63)(49,64)(50,68)(51,69)(52,70)(53,74)(54,75)(55,76)(56,71)(57,72)
(58,73);;
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, s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3, 
s4*s2*s3*s4*s3*s2*s3*s4*s2*s3*s4*s3*s2*s3, 
s4*s2*s3*s4*s3*s4*s3*s4*s3*s4*s2*s3*s4*s3*s4*s3*s4*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)(24,25)
(26,29)(27,31)(28,30)(33,34)(35,38)(36,40)(37,39)(42,43)(44,47)(45,49)(46,48)
(51,52)(53,56)(54,58)(55,57)(60,61)(62,65)(63,67)(64,66)(69,70)(71,74)(72,76)
(73,75);
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)!( 8,11)( 9,12)(10,13)(17,20)(18,21)(19,22)(23,32)(24,33)(25,34)
(26,38)(27,39)(28,40)(29,35)(30,36)(31,37)(41,59)(42,60)(43,61)(44,65)(45,66)
(46,67)(47,62)(48,63)(49,64)(50,68)(51,69)(52,70)(53,74)(54,75)(55,76)(56,71)
(57,72)(58,73);
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, 
s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3, 
s4*s2*s3*s4*s3*s2*s3*s4*s2*s3*s4*s3*s2*s3, 
s4*s2*s3*s4*s3*s4*s3*s4*s3*s4*s2*s3*s4*s3*s4*s3*s4*s3 >;

to this polytope