Polytope of Type {4,24}

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

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

Permutation Representation (Magma) :

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

References : None.
to this polytope