Polytope of Type {2,24,6}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,24,6}*576a
if this polytope has a name.
Group : SmallGroup(576,6554)
Rank : 4
Schlafli Type : {2,24,6}
Number of vertices, edges, etc : 2, 24, 72, 6
Order of s₀s₁s₂s₃ : 24
Order of s₀s₁s₂s₃s₂s₁ : 2
Special Properties :
   Degenerate
   Universal
   Orientable
   Flat
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   {2,24,6,2} of size 1152
   {2,24,6,3} of size 1728
Vertex Figure Of :
   {2,2,24,6} of size 1152
   {3,2,24,6} of size 1728
Quotients (Maximal Quotients in Boldface) :
   2-fold quotients : {2,12,6}*288a
   3-fold quotients : {2,24,2}*192, {2,8,6}*192
   4-fold quotients : {2,6,6}*144a
   6-fold quotients : {2,12,2}*96, {2,4,6}*96a
   9-fold quotients : {2,8,2}*64
   12-fold quotients : {2,2,6}*48, {2,6,2}*48
   18-fold quotients : {2,4,2}*32
   24-fold quotients : {2,2,3}*24, {2,3,2}*24
   36-fold quotients : {2,2,2}*16
Covers (Minimal Covers in Boldface) :
   2-fold covers : {4,24,6}*1152c, {2,24,12}*1152a, {2,48,6}*1152b
   3-fold covers : {2,72,6}*1728a, {2,24,18}*1728a, {2,24,6}*1728b, {6,24,6}*1728b, {6,24,6}*1728c, {2,24,6}*1728f
Permutation Representation (GAP) :

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

Finitely Presented Group Representation (GAP) :

F := FreeGroup("s0","s1","s2","s3");;
s0 := F.1;;  s1 := F.2;;  s2 := F.3;;  s3 := F.4;;  
rels := [ s0*s0, s1*s1, s2*s2, s3*s3, s0*s1*s0*s1, 
s0*s2*s0*s2, s0*s3*s0*s3, s1*s3*s1*s3, 
s1*s2*s3*s2*s1*s2*s3*s2, s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3, 
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2 ];;
poly := F / rels;;

Permutation Representation (Magma) :

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

Finitely Presented Group Representation (Magma) :

poly<s0,s1,s2,s3> := Group< s0,s1,s2,s3 | s0*s0, s1*s1, s2*s2, 
s3*s3, s0*s1*s0*s1, s0*s2*s0*s2, s0*s3*s0*s3, 
s1*s3*s1*s3, s1*s2*s3*s2*s1*s2*s3*s2, 
s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3, 
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2 >;

to this polytope