Polytope of Type {24,4}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {24,4}*192c
if this polytope has a name.
Group : SmallGroup(192,961)
Rank : 3
Schlafli Type : {24,4}
Number of vertices, edges, etc : 24, 48, 4
Order of s₀s₁s₂ : 24
Order of s₀s₁s₂s₁ : 4
Special Properties :
   Compact Hyperbolic Quotient
   Locally Spherical
   Non-Orientable
   Flat
   Self-Petrie
Related Polytopes :
   Facet
   Vertex Figure
   Dual
   Petrial
   Skewing Operation
Facet Of :
   {24,4,2} of size 384
Vertex Figure Of :
   {2,24,4} 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
   {6,24,4} of size 1152
   {6,24,4} of size 1152
   {10,24,4} of size 1920
Quotients (Maximal Quotients in Boldface) :
   2-fold quotients : {12,4}*96b
   4-fold quotients : {6,4}*48c
   8-fold quotients : {3,4}*24
Covers (Minimal Covers in Boldface) :
   2-fold covers : {48,4}*384c, {48,4}*384d, {24,4}*384c
   3-fold covers : {72,4}*576c
   4-fold covers : {24,4}*768e, {96,4}*768c, {96,4}*768d, {24,8}*768i, {24,8}*768k, {24,4}*768i, {48,4}*768c, {48,4}*768d
   5-fold covers : {120,4}*960c
   6-fold covers : {144,4}*1152c, {144,4}*1152d, {72,4}*1152c, {24,12}*1152o, {24,12}*1152p
   7-fold covers : {168,4}*1344c
   9-fold covers : {216,4}*1728c
   10-fold covers : {240,4}*1920c, {240,4}*1920d, {24,20}*1920c, {120,4}*1920c
Permutation Representation (GAP) :

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

Permutation Representation (Magma) :

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

References : None.
to this polytope