Polytope of Type {4,24}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {4,24}*192d
if this polytope has a name.
Group : SmallGroup(192,961)
Rank : 3
Schlafli Type : {4,24}
Number of vertices, edges, etc : 4, 48, 24
Order of s₀s₁s₂ : 24
Order of s₀s₁s₂s₁ : 4
Special Properties :
   Compact Hyperbolic Quotient
   Locally Spherical
   Non-Orientable
   Flat
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   {4,24,2} of size 384
   {4,24,4} of size 768
   {4,24,4} of size 768
   {4,24,4} of size 768
   {4,24,4} of size 768
   {4,24,6} of size 1152
   {4,24,6} of size 1152
   {4,24,10} of size 1920
Vertex Figure Of :
   {2,4,24} of size 384
Quotients (Maximal Quotients in Boldface) :
   2-fold quotients : {4,12}*96b
   4-fold quotients : {4,6}*48c
   8-fold quotients : {4,3}*24
Covers (Minimal Covers in Boldface) :
   2-fold covers : {4,24}*384c
   3-fold covers : {4,72}*576d
   4-fold covers : {4,24}*768f, {8,24}*768i, {8,24}*768k, {4,24}*768i, {4,48}*768c, {4,48}*768d
   5-fold covers : {4,120}*960d
   6-fold covers : {4,72}*1152c, {12,24}*1152o, {12,24}*1152p
   7-fold covers : {4,168}*1344d
   9-fold covers : {4,216}*1728d
   10-fold covers : {20,24}*1920c, {4,120}*1920c
Permutation Representation (GAP) :

s0 := ( 1,14)( 2,13)( 3,16)( 4,15)( 5,18)( 6,17)( 7,20)( 8,19)( 9,22)(10,21)
(11,24)(12,23)(25,38)(26,37)(27,40)(28,39)(29,42)(30,41)(31,44)(32,43)(33,46)
(34,45)(35,48)(36,47)(49,62)(50,61)(51,64)(52,63)(53,66)(54,65)(55,68)(56,67)
(57,70)(58,69)(59,72)(60,71)(73,86)(74,85)(75,88)(76,87)(77,90)(78,89)(79,92)
(80,91)(81,94)(82,93)(83,96)(84,95);;
s1 := ( 2, 3)( 5, 9)( 6,11)( 7,10)( 8,12)(14,15)(17,21)(18,23)(19,22)(20,24)
(25,37)(26,39)(27,38)(28,40)(29,45)(30,47)(31,46)(32,48)(33,41)(34,43)(35,42)
(36,44)(49,73)(50,75)(51,74)(52,76)(53,81)(54,83)(55,82)(56,84)(57,77)(58,79)
(59,78)(60,80)(61,85)(62,87)(63,86)(64,88)(65,93)(66,95)(67,94)(68,96)(69,89)
(70,91)(71,90)(72,92);;
s2 := ( 1,53)( 2,54)( 3,56)( 4,55)( 5,49)( 6,50)( 7,52)( 8,51)( 9,57)(10,58)
(11,60)(12,59)(13,65)(14,66)(15,68)(16,67)(17,61)(18,62)(19,64)(20,63)(21,69)
(22,70)(23,72)(24,71)(25,89)(26,90)(27,92)(28,91)(29,85)(30,86)(31,88)(32,87)
(33,93)(34,94)(35,96)(36,95)(37,77)(38,78)(39,80)(40,79)(41,73)(42,74)(43,76)
(44,75)(45,81)(46,82)(47,84)(48,83);;
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*s0*s1, 
s0*s1*s2*s1*s2*s1*s0*s1*s2*s1*s2*s1, 
s2*s1*s2*s1*s2*s1*s2*s1*s0*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s0*s1*s0 ];;
poly := F / rels;;

Permutation Representation (Magma) :

s0 := Sym(96)!( 1,14)( 2,13)( 3,16)( 4,15)( 5,18)( 6,17)( 7,20)( 8,19)( 9,22)
(10,21)(11,24)(12,23)(25,38)(26,37)(27,40)(28,39)(29,42)(30,41)(31,44)(32,43)
(33,46)(34,45)(35,48)(36,47)(49,62)(50,61)(51,64)(52,63)(53,66)(54,65)(55,68)
(56,67)(57,70)(58,69)(59,72)(60,71)(73,86)(74,85)(75,88)(76,87)(77,90)(78,89)
(79,92)(80,91)(81,94)(82,93)(83,96)(84,95);
s1 := Sym(96)!( 2, 3)( 5, 9)( 6,11)( 7,10)( 8,12)(14,15)(17,21)(18,23)(19,22)
(20,24)(25,37)(26,39)(27,38)(28,40)(29,45)(30,47)(31,46)(32,48)(33,41)(34,43)
(35,42)(36,44)(49,73)(50,75)(51,74)(52,76)(53,81)(54,83)(55,82)(56,84)(57,77)
(58,79)(59,78)(60,80)(61,85)(62,87)(63,86)(64,88)(65,93)(66,95)(67,94)(68,96)
(69,89)(70,91)(71,90)(72,92);
s2 := Sym(96)!( 1,53)( 2,54)( 3,56)( 4,55)( 5,49)( 6,50)( 7,52)( 8,51)( 9,57)
(10,58)(11,60)(12,59)(13,65)(14,66)(15,68)(16,67)(17,61)(18,62)(19,64)(20,63)
(21,69)(22,70)(23,72)(24,71)(25,89)(26,90)(27,92)(28,91)(29,85)(30,86)(31,88)
(32,87)(33,93)(34,94)(35,96)(36,95)(37,77)(38,78)(39,80)(40,79)(41,73)(42,74)
(43,76)(44,75)(45,81)(46,82)(47,84)(48,83);
poly := sub<Sym(96)|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*s0*s1, 
s0*s1*s2*s1*s2*s1*s0*s1*s2*s1*s2*s1, 
s2*s1*s2*s1*s2*s1*s2*s1*s0*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s0*s1*s0 >;

References : None.
to this polytope