Polytope of Type {4,24}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {4,24}*192a
Also Known As : {4,24|2}. if this polytope has another name.
Group : SmallGroup(192,291)
Rank : 3
Schlafli Type : {4,24}
Number of vertices, edges, etc : 4, 48, 24
Order of s₀s₁s₂ : 24
Order of s₀s₁s₂s₁ : 2
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
   {4,24,3} 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
   {3,4,24} of size 1152
   {6,4,24} of size 1728
   {10,4,24} of size 1920
Quotients (Maximal Quotients in Boldface) :
   2-fold quotients : {4,12}*96a, {2,24}*96
   3-fold quotients : {4,8}*64a
   4-fold quotients : {2,12}*48, {4,6}*48a
   6-fold quotients : {4,4}*32, {2,8}*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}*384a, {8,24}*384b, {4,48}*384a, {4,48}*384b
   3-fold covers : {4,72}*576a, {12,24}*576c, {12,24}*576d
   4-fold covers : {8,24}*768a, {4,24}*768a, {8,24}*768d, {4,48}*768a, {4,48}*768b, {16,24}*768a, {16,24}*768b, {8,48}*768c, {8,48}*768d, {16,24}*768d, {8,48}*768e, {8,48}*768f, {16,24}*768f, {4,96}*768a, {4,96}*768b, {4,24}*768i
   5-fold covers : {20,24}*960a, {4,120}*960a
   6-fold covers : {4,72}*1152a, {12,24}*1152a, {12,24}*1152b, {8,72}*1152b, {8,72}*1152c, {24,24}*1152a, {24,24}*1152b, {24,24}*1152h, {24,24}*1152i, {4,144}*1152a, {12,48}*1152a, {12,48}*1152b, {4,144}*1152b, {12,48}*1152d, {12,48}*1152e
   7-fold covers : {28,24}*1344a, {4,168}*1344a
   9-fold covers : {4,216}*1728a, {12,72}*1728a, {12,72}*1728b, {36,24}*1728c, {12,24}*1728c, {12,24}*1728d, {12,24}*1728o, {4,24}*1728e, {4,24}*1728f, {12,24}*1728u
   10-fold covers : {4,120}*1920a, {20,24}*1920a, {8,120}*1920b, {8,120}*1920c, {40,24}*1920a, {40,24}*1920b, {4,240}*1920a, {20,48}*1920a, {4,240}*1920b, {20,48}*1920b
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)(13,61)(14,62)(15,63)(16,64)(17,65)(18,66)(19,67)(20,68)(21,69)
(22,70)(23,71)(24,72)(25,79)(26,80)(27,81)(28,82)(29,83)(30,84)(31,73)(32,74)
(33,75)(34,76)(35,77)(36,78)(37,91)(38,92)(39,93)(40,94)(41,95)(42,96)(43,85)
(44,86)(45,87)(46,88)(47,89)(48,90);;
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, 8)(10,11)(13,17)(14,16)(15,18)(19,23)(20,22)(21,24)
(25,38)(26,37)(27,39)(28,41)(29,40)(30,42)(31,44)(32,43)(33,45)(34,47)(35,46)
(36,48)(49,50)(52,53)(55,56)(58,59)(61,65)(62,64)(63,66)(67,71)(68,70)(69,72)
(73,86)(74,85)(75,87)(76,89)(77,88)(78,90)(79,92)(80,91)(81,93)(82,95)(83,94)
(84,96);;
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*s0*s1*s2*s1, s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2 ];;
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)(13,61)(14,62)(15,63)(16,64)(17,65)(18,66)(19,67)(20,68)
(21,69)(22,70)(23,71)(24,72)(25,79)(26,80)(27,81)(28,82)(29,83)(30,84)(31,73)
(32,74)(33,75)(34,76)(35,77)(36,78)(37,91)(38,92)(39,93)(40,94)(41,95)(42,96)
(43,85)(44,86)(45,87)(46,88)(47,89)(48,90);
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, 8)(10,11)(13,17)(14,16)(15,18)(19,23)(20,22)
(21,24)(25,38)(26,37)(27,39)(28,41)(29,40)(30,42)(31,44)(32,43)(33,45)(34,47)
(35,46)(36,48)(49,50)(52,53)(55,56)(58,59)(61,65)(62,64)(63,66)(67,71)(68,70)
(69,72)(73,86)(74,85)(75,87)(76,89)(77,88)(78,90)(79,92)(80,91)(81,93)(82,95)
(83,94)(84,96);
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*s0*s1*s2*s1, s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2 >;

References : None.
to this polytope