Polytope of Type {4,24}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {4,24}*384b
if this polytope has a name.
Group : SmallGroup(384,1706)
Rank : 3
Schlafli Type : {4,24}
Number of vertices, edges, etc : 8, 96, 48
Order of s₀s₁s₂ : 12
Order of s₀s₁s₂s₁ : 4
Special Properties :
   Compact Hyperbolic Quotient
   Locally Spherical
   Orientable
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   {4,24,2} of size 768
Vertex Figure Of :
   {2,4,24} of size 768
Quotients (Maximal Quotients in Boldface) :
   2-fold quotients : {4,12}*192a
   3-fold quotients : {4,8}*128b
   4-fold quotients : {4,12}*96a
   6-fold quotients : {4,4}*64
   8-fold quotients : {2,12}*48, {4,6}*48a
   12-fold quotients : {4,4}*32
   16-fold quotients : {2,6}*24
   24-fold quotients : {2,4}*16, {4,2}*16
   32-fold quotients : {2,3}*12
   48-fold quotients : {2,2}*8
Covers (Minimal Covers in Boldface) :
   2-fold covers : {8,24}*768b, {4,24}*768a, {8,24}*768c, {4,24}*768b, {8,24}*768e, {4,24}*768d, {8,24}*768g
   3-fold covers : {4,72}*1152b, {12,24}*1152e, {12,24}*1152f
   5-fold covers : {4,120}*1920b, {20,24}*1920b
Permutation Representation (GAP) :

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

Permutation Representation (Magma) :

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

References : None.
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