Polytope of Type {3,24}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {3,24}*576
if this polytope has a name.
Group : SmallGroup(576,5053)
Rank : 3
Schlafli Type : {3,24}
Number of vertices, edges, etc : 12, 144, 96
Order of s₀s₁s₂ : 6
Order of s₀s₁s₂s₁ : 24
Special Properties :
   Compact Hyperbolic Quotient
   Locally Spherical
   Orientable
Related Polytopes :
   Facet
   Vertex Figure
   Dual
   Petrial
Facet Of :
   {3,24,2} of size 1152
Vertex Figure Of :
   {2,3,24} of size 1152
Quotients (Maximal Quotients in Boldface) :
   3-fold quotients : {3,8}*192
   4-fold quotients : {3,12}*144
   12-fold quotients : {3,4}*48
   16-fold quotients : {3,6}*36
   24-fold quotients : {3,4}*24
   48-fold quotients : {3,2}*12
Covers (Minimal Covers in Boldface) :
   2-fold covers : {3,24}*1152a, {6,24}*1152a, {6,24}*1152b
   3-fold covers : {9,24}*1728, {3,24}*1728
Permutation Representation (GAP) :

s0 := ( 3, 4)( 5,12)( 6,11)( 7, 9)( 8,10)(13,14)(17,33)(18,34)(19,36)(20,35)
(21,44)(22,43)(23,41)(24,42)(25,39)(26,40)(27,38)(28,37)(29,46)(30,45)(31,47)
(32,48);;
s1 := ( 1,17)( 2,19)( 3,18)( 4,20)( 5,24)( 6,22)( 7,23)( 8,21)( 9,32)(10,30)
(11,31)(12,29)(13,28)(14,26)(15,27)(16,25)(34,35)(37,40)(41,48)(42,46)(43,47)
(44,45);;
s2 := ( 1,15)( 2,16)( 3,13)( 4,14)( 5,11)( 6,12)( 7, 9)( 8,10)(17,47)(18,48)
(19,45)(20,46)(21,43)(22,44)(23,41)(24,42)(25,39)(26,40)(27,37)(28,38)(29,35)
(30,36)(31,33)(32,34);;
poly := Group([s0,s1,s2]);;

Finitely Presented Group Representation (GAP) :

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

Permutation Representation (Magma) :

s0 := Sym(48)!( 3, 4)( 5,12)( 6,11)( 7, 9)( 8,10)(13,14)(17,33)(18,34)(19,36)
(20,35)(21,44)(22,43)(23,41)(24,42)(25,39)(26,40)(27,38)(28,37)(29,46)(30,45)
(31,47)(32,48);
s1 := Sym(48)!( 1,17)( 2,19)( 3,18)( 4,20)( 5,24)( 6,22)( 7,23)( 8,21)( 9,32)
(10,30)(11,31)(12,29)(13,28)(14,26)(15,27)(16,25)(34,35)(37,40)(41,48)(42,46)
(43,47)(44,45);
s2 := Sym(48)!( 1,15)( 2,16)( 3,13)( 4,14)( 5,11)( 6,12)( 7, 9)( 8,10)(17,47)
(18,48)(19,45)(20,46)(21,43)(22,44)(23,41)(24,42)(25,39)(26,40)(27,37)(28,38)
(29,35)(30,36)(31,33)(32,34);
poly := sub<Sym(48)|s0,s1,s2>;

Finitely Presented Group Representation (Magma) :

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

References : None.
to this polytope