Polytope of Type {24,4}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {24,4}*192b
if this polytope has a name.
Group : SmallGroup(192,306)
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
   Orientable
   Flat
   Self-Petrie
Related Polytopes :
   Facet
   Vertex Figure
   Dual
   Petrial
Facet Of :
   {24,4,2} of size 384
   {24,4,4} of size 768
   {24,4,6} of size 1152
   {24,4,10} of size 1920
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
   {6,24,4} of size 1152
   {10,24,4} of size 1920
Quotients (Maximal Quotients in Boldface) :
   2-fold quotients : {12,4}*96a
   3-fold quotients : {8,4}*64b
   4-fold quotients : {12,2}*48, {6,4}*48a
   6-fold quotients : {4,4}*32
   8-fold quotients : {6,2}*24
   12-fold quotients : {2,4}*16, {4,2}*16
   16-fold quotients : {3,2}*12
   24-fold quotients : {2,2}*8
Covers (Minimal Covers in Boldface) :
   2-fold covers : {24,4}*384a, {24,8}*384c, {24,8}*384d
   3-fold covers : {72,4}*576b, {24,12}*576e, {24,12}*576f
   4-fold covers : {24,8}*768a, {24,4}*768a, {24,8}*768d, {48,4}*768a, {48,4}*768b, {48,8}*768a, {48,8}*768b, {24,16}*768c, {24,16}*768e, {24,4}*768j
   5-fold covers : {24,20}*960b, {120,4}*960b
   6-fold covers : {72,4}*1152a, {24,12}*1152a, {24,12}*1152b, {72,8}*1152a, {24,24}*1152d, {24,24}*1152i, {72,8}*1152d, {24,24}*1152k, {24,24}*1152l
   7-fold covers : {24,28}*1344b, {168,4}*1344b
   9-fold covers : {216,4}*1728b, {72,12}*1728c, {72,12}*1728d, {24,36}*1728d, {24,12}*1728e, {24,12}*1728f, {24,12}*1728p, {24,4}*1728g, {24,4}*1728h, {24,12}*1728x
   10-fold covers : {120,4}*1920a, {24,20}*1920a, {120,8}*1920a, {24,40}*1920c, {120,8}*1920d, {24,40}*1920d
Permutation Representation (GAP) :

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

References : None.
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