Polytope of Type {24,4,2,5}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {24,4,2,5}*1920b
if this polytope has a name.
Group : SmallGroup(1920,150682)
Rank : 5
Schlafli Type : {24,4,2,5}
Number of vertices, edges, etc : 24, 48, 4, 5, 5
Order of s₀s₁s₂s₃s₄ : 120
Order of s₀s₁s₂s₃s₄s₃s₂s₁ : 2
Special Properties :
   Degenerate
   Universal
   Orientable
   Flat
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   None in this Atlas
Vertex Figure Of :
   None in this Atlas
Quotients (Maximal Quotients in Boldface) :
   2-fold quotients : {12,4,2,5}*960a
   3-fold quotients : {8,4,2,5}*640b
   4-fold quotients : {12,2,2,5}*480, {6,4,2,5}*480a
   6-fold quotients : {4,4,2,5}*320
   8-fold quotients : {6,2,2,5}*240
   12-fold quotients : {2,4,2,5}*160, {4,2,2,5}*160
   16-fold quotients : {3,2,2,5}*120
   24-fold quotients : {2,2,2,5}*80
Covers (Minimal Covers in Boldface) :
   None in this atlas.
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);;
s3 := ( 98, 99)(100,101);;
s4 := ( 97, 98)( 99,100);;
poly := Group([s0,s1,s2,s3,s4]);;

Finitely Presented Group Representation (GAP) :

F := FreeGroup("s0","s1","s2","s3","s4");;
s0 := F.1;;  s1 := F.2;;  s2 := F.3;;  s3 := F.4;;  s4 := F.5;;  
rels := [ s0*s0, s1*s1, s2*s2, s3*s3, s4*s4, s0*s2*s0*s2, 
s0*s3*s0*s3, s1*s3*s1*s3, s2*s3*s2*s3, 
s0*s4*s0*s4, s1*s4*s1*s4, s2*s4*s2*s4, 
s1*s2*s1*s2*s1*s2*s1*s2, s3*s4*s3*s4*s3*s4*s3*s4*s3*s4, 
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(101)!( 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(101)!( 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(101)!( 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);
s3 := Sym(101)!( 98, 99)(100,101);
s4 := Sym(101)!( 97, 98)( 99,100);
poly := sub<Sym(101)|s0,s1,s2,s3,s4>;

Finitely Presented Group Representation (Magma) :

poly<s0,s1,s2,s3,s4> := Group< s0,s1,s2,s3,s4 | s0*s0, s1*s1, s2*s2, 
s3*s3, s4*s4, s0*s2*s0*s2, s0*s3*s0*s3, 
s1*s3*s1*s3, s2*s3*s2*s3, s0*s4*s0*s4, 
s1*s4*s1*s4, s2*s4*s2*s4, s1*s2*s1*s2*s1*s2*s1*s2, 
s3*s4*s3*s4*s3*s4*s3*s4*s3*s4, 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 >;

to this polytope