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

Permutation Representation (Magma) :

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

to this polytope