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

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,6,24,2}*1152a
if this polytope has a name.
Group : SmallGroup(1152,152550)
Rank : 5
Schlafli Type : {2,6,24,2}
Number of vertices, edges, etc : 2, 6, 72, 24, 2
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 : {2,6,12,2}*576c
   3-fold quotients : {2,6,8,2}*384
   4-fold quotients : {2,6,6,2}*288c
   6-fold quotients : {2,6,4,2}*192a
   8-fold quotients : {2,3,6,2}*144
   9-fold quotients : {2,2,8,2}*128
   12-fold quotients : {2,6,2,2}*96
   18-fold quotients : {2,2,4,2}*64
   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)( 6, 9)( 7,11)( 8,10)(13,14)(15,18)(16,20)(17,19)(22,23)(24,27)
(25,29)(26,28)(31,32)(33,36)(34,38)(35,37)(40,41)(42,45)(43,47)(44,46)(49,50)
(51,54)(52,56)(53,55)(58,59)(60,63)(61,65)(62,64)(67,68)(69,72)(70,74)
(71,73);;
s2 := ( 3,43)( 4,42)( 5,44)( 6,40)( 7,39)( 8,41)( 9,46)(10,45)(11,47)(12,52)
(13,51)(14,53)(15,49)(16,48)(17,50)(18,55)(19,54)(20,56)(21,70)(22,69)(23,71)
(24,67)(25,66)(26,68)(27,73)(28,72)(29,74)(30,61)(31,60)(32,62)(33,58)(34,57)
(35,59)(36,64)(37,63)(38,65);;
s3 := ( 6, 9)( 7,10)( 8,11)(15,18)(16,19)(17,20)(21,30)(22,31)(23,32)(24,36)
(25,37)(26,38)(27,33)(28,34)(29,35)(39,57)(40,58)(41,59)(42,63)(43,64)(44,65)
(45,60)(46,61)(47,62)(48,66)(49,67)(50,68)(51,72)(52,73)(53,74)(54,69)(55,70)
(56,71);;
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, 
s3*s1*s2*s3*s2*s1*s2*s3*s1*s2*s3*s2*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)( 6, 9)( 7,11)( 8,10)(13,14)(15,18)(16,20)(17,19)(22,23)
(24,27)(25,29)(26,28)(31,32)(33,36)(34,38)(35,37)(40,41)(42,45)(43,47)(44,46)
(49,50)(51,54)(52,56)(53,55)(58,59)(60,63)(61,65)(62,64)(67,68)(69,72)(70,74)
(71,73);
s2 := Sym(76)!( 3,43)( 4,42)( 5,44)( 6,40)( 7,39)( 8,41)( 9,46)(10,45)(11,47)
(12,52)(13,51)(14,53)(15,49)(16,48)(17,50)(18,55)(19,54)(20,56)(21,70)(22,69)
(23,71)(24,67)(25,66)(26,68)(27,73)(28,72)(29,74)(30,61)(31,60)(32,62)(33,58)
(34,57)(35,59)(36,64)(37,63)(38,65);
s3 := Sym(76)!( 6, 9)( 7,10)( 8,11)(15,18)(16,19)(17,20)(21,30)(22,31)(23,32)
(24,36)(25,37)(26,38)(27,33)(28,34)(29,35)(39,57)(40,58)(41,59)(42,63)(43,64)
(44,65)(45,60)(46,61)(47,62)(48,66)(49,67)(50,68)(51,72)(52,73)(53,74)(54,69)
(55,70)(56,71);
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, 
s3*s1*s2*s3*s2*s1*s2*s3*s1*s2*s3*s2*s1*s2, 
s3*s1*s2*s3*s2*s3*s2*s3*s2*s3*s1*s2*s3*s2*s3*s2*s3*s2 >;

to this polytope