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}*1152a
if this polytope has a name.
Group : SmallGroup(1152,152550)
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}*576c
   3-fold quotients : {2,2,8,6}*384
   4-fold quotients : {2,2,6,6}*288b
   6-fold quotients : {2,2,4,6}*192a
   8-fold quotients : {2,2,6,3}*144
   9-fold quotients : {2,2,8,2}*128
   12-fold quotients : {2,2,2,6}*96
   18-fold quotients : {2,2,4,2}*64
   24-fold quotients : {2,2,2,3}*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 := ( 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);;
s3 := ( 5,44)( 6,46)( 7,45)( 8,41)( 9,43)(10,42)(11,47)(12,49)(13,48)(14,53)
(15,55)(16,54)(17,50)(18,52)(19,51)(20,56)(21,58)(22,57)(23,71)(24,73)(25,72)
(26,68)(27,70)(28,69)(29,74)(30,76)(31,75)(32,62)(33,64)(34,63)(35,59)(36,61)
(37,60)(38,65)(39,67)(40,66);;
s4 := ( 5, 6)( 8,12)( 9,11)(10,13)(14,15)(17,21)(18,20)(19,22)(23,24)(26,30)
(27,29)(28,31)(32,33)(35,39)(36,38)(37,40)(41,42)(44,48)(45,47)(46,49)(50,51)
(53,57)(54,56)(55,58)(59,60)(62,66)(63,65)(64,67)(68,69)(71,75)(72,74)
(73,76);;
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, s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4, 
s4*s2*s3*s4*s3*s2*s3*s4*s2*s3*s4*s3*s2*s3, 
s4*s2*s3*s2*s3*s2*s3*s2*s3*s4*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)!( 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);
s3 := Sym(76)!( 5,44)( 6,46)( 7,45)( 8,41)( 9,43)(10,42)(11,47)(12,49)(13,48)
(14,53)(15,55)(16,54)(17,50)(18,52)(19,51)(20,56)(21,58)(22,57)(23,71)(24,73)
(25,72)(26,68)(27,70)(28,69)(29,74)(30,76)(31,75)(32,62)(33,64)(34,63)(35,59)
(36,61)(37,60)(38,65)(39,67)(40,66);
s4 := Sym(76)!( 5, 6)( 8,12)( 9,11)(10,13)(14,15)(17,21)(18,20)(19,22)(23,24)
(26,30)(27,29)(28,31)(32,33)(35,39)(36,38)(37,40)(41,42)(44,48)(45,47)(46,49)
(50,51)(53,57)(54,56)(55,58)(59,60)(62,66)(63,65)(64,67)(68,69)(71,75)(72,74)
(73,76);
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, 
s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4, 
s4*s2*s3*s4*s3*s2*s3*s4*s2*s3*s4*s3*s2*s3, 
s4*s2*s3*s2*s3*s2*s3*s2*s3*s4*s2*s3*s2*s3*s2*s3*s2*s3 >;

to this polytope