Polytope of Type {24,6}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {24,6}*1152f
if this polytope has a name.
Group : SmallGroup(1152,155791)
Rank : 3
Schlafli Type : {24,6}
Number of vertices, edges, etc : 96, 288, 24
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 :
   None in this Atlas
Vertex Figure Of :
   None in this Atlas
Quotients (Maximal Quotients in Boldface) :
   3-fold quotients : {8,6}*384d
   4-fold quotients : {12,6}*288b
   6-fold quotients : {8,6}*192a
   8-fold quotients : {12,3}*144
   12-fold quotients : {4,6}*96
   16-fold quotients : {6,6}*72b
   24-fold quotients : {4,3}*48, {4,6}*48b, {4,6}*48c
   32-fold quotients : {6,3}*36
   48-fold quotients : {4,3}*24, {2,6}*24
   96-fold quotients : {2,3}*12
   144-fold quotients : {2,2}*8
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :

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

Permutation Representation (Magma) :

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

References : None.
to this polytope