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

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {5,2,4,24}*1920d
if this polytope has a name.
Group : SmallGroup(1920,238608)
Rank : 5
Schlafli Type : {5,2,4,24}
Number of vertices, edges, etc : 5, 5, 4, 48, 24
Order of s0s1s2s3s4 : 120
Order of s0s1s2s3s4s3s2s1 : 2
Special Properties :
   Degenerate
   Universal
   Non-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 : {5,2,4,12}*960b
   4-fold quotients : {5,2,4,6}*480c
   8-fold quotients : {5,2,4,3}*240
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :
s0 := (2,3)(4,5);;
s1 := (1,2)(3,4);;
s2 := (  6, 19)(  7, 18)(  8, 21)(  9, 20)( 10, 23)( 11, 22)( 12, 25)( 13, 24)
( 14, 27)( 15, 26)( 16, 29)( 17, 28)( 30, 43)( 31, 42)( 32, 45)( 33, 44)
( 34, 47)( 35, 46)( 36, 49)( 37, 48)( 38, 51)( 39, 50)( 40, 53)( 41, 52)
( 54, 67)( 55, 66)( 56, 69)( 57, 68)( 58, 71)( 59, 70)( 60, 73)( 61, 72)
( 62, 75)( 63, 74)( 64, 77)( 65, 76)( 78, 91)( 79, 90)( 80, 93)( 81, 92)
( 82, 95)( 83, 94)( 84, 97)( 85, 96)( 86, 99)( 87, 98)( 88,101)( 89,100);;
s3 := (  7,  8)( 10, 14)( 11, 16)( 12, 15)( 13, 17)( 19, 20)( 22, 26)( 23, 28)
( 24, 27)( 25, 29)( 30, 42)( 31, 44)( 32, 43)( 33, 45)( 34, 50)( 35, 52)
( 36, 51)( 37, 53)( 38, 46)( 39, 48)( 40, 47)( 41, 49)( 54, 78)( 55, 80)
( 56, 79)( 57, 81)( 58, 86)( 59, 88)( 60, 87)( 61, 89)( 62, 82)( 63, 84)
( 64, 83)( 65, 85)( 66, 90)( 67, 92)( 68, 91)( 69, 93)( 70, 98)( 71,100)
( 72, 99)( 73,101)( 74, 94)( 75, 96)( 76, 95)( 77, 97);;
s4 := (  6, 58)(  7, 59)(  8, 61)(  9, 60)( 10, 54)( 11, 55)( 12, 57)( 13, 56)
( 14, 62)( 15, 63)( 16, 65)( 17, 64)( 18, 70)( 19, 71)( 20, 73)( 21, 72)
( 22, 66)( 23, 67)( 24, 69)( 25, 68)( 26, 74)( 27, 75)( 28, 77)( 29, 76)
( 30, 94)( 31, 95)( 32, 97)( 33, 96)( 34, 90)( 35, 91)( 36, 93)( 37, 92)
( 38, 98)( 39, 99)( 40,101)( 41,100)( 42, 82)( 43, 83)( 44, 85)( 45, 84)
( 46, 78)( 47, 79)( 48, 81)( 49, 80)( 50, 86)( 51, 87)( 52, 89)( 53, 88);;
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, 
s1*s2*s1*s2, s0*s3*s0*s3, s1*s3*s1*s3, 
s0*s4*s0*s4, s1*s4*s1*s4, s2*s4*s2*s4, 
s2*s3*s2*s3*s2*s3*s2*s3, s0*s1*s0*s1*s0*s1*s0*s1*s0*s1, 
s2*s3*s4*s3*s4*s3*s2*s3*s4*s3*s4*s3, 
s4*s3*s4*s3*s4*s3*s4*s3*s2*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s2*s3*s2 ];;
poly := F / rels;;
 
Permutation Representation (Magma) :
s0 := Sym(101)!(2,3)(4,5);
s1 := Sym(101)!(1,2)(3,4);
s2 := Sym(101)!(  6, 19)(  7, 18)(  8, 21)(  9, 20)( 10, 23)( 11, 22)( 12, 25)
( 13, 24)( 14, 27)( 15, 26)( 16, 29)( 17, 28)( 30, 43)( 31, 42)( 32, 45)
( 33, 44)( 34, 47)( 35, 46)( 36, 49)( 37, 48)( 38, 51)( 39, 50)( 40, 53)
( 41, 52)( 54, 67)( 55, 66)( 56, 69)( 57, 68)( 58, 71)( 59, 70)( 60, 73)
( 61, 72)( 62, 75)( 63, 74)( 64, 77)( 65, 76)( 78, 91)( 79, 90)( 80, 93)
( 81, 92)( 82, 95)( 83, 94)( 84, 97)( 85, 96)( 86, 99)( 87, 98)( 88,101)
( 89,100);
s3 := Sym(101)!(  7,  8)( 10, 14)( 11, 16)( 12, 15)( 13, 17)( 19, 20)( 22, 26)
( 23, 28)( 24, 27)( 25, 29)( 30, 42)( 31, 44)( 32, 43)( 33, 45)( 34, 50)
( 35, 52)( 36, 51)( 37, 53)( 38, 46)( 39, 48)( 40, 47)( 41, 49)( 54, 78)
( 55, 80)( 56, 79)( 57, 81)( 58, 86)( 59, 88)( 60, 87)( 61, 89)( 62, 82)
( 63, 84)( 64, 83)( 65, 85)( 66, 90)( 67, 92)( 68, 91)( 69, 93)( 70, 98)
( 71,100)( 72, 99)( 73,101)( 74, 94)( 75, 96)( 76, 95)( 77, 97);
s4 := Sym(101)!(  6, 58)(  7, 59)(  8, 61)(  9, 60)( 10, 54)( 11, 55)( 12, 57)
( 13, 56)( 14, 62)( 15, 63)( 16, 65)( 17, 64)( 18, 70)( 19, 71)( 20, 73)
( 21, 72)( 22, 66)( 23, 67)( 24, 69)( 25, 68)( 26, 74)( 27, 75)( 28, 77)
( 29, 76)( 30, 94)( 31, 95)( 32, 97)( 33, 96)( 34, 90)( 35, 91)( 36, 93)
( 37, 92)( 38, 98)( 39, 99)( 40,101)( 41,100)( 42, 82)( 43, 83)( 44, 85)
( 45, 84)( 46, 78)( 47, 79)( 48, 81)( 49, 80)( 50, 86)( 51, 87)( 52, 89)
( 53, 88);
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, s1*s2*s1*s2, 
s0*s3*s0*s3, s1*s3*s1*s3, s0*s4*s0*s4, 
s1*s4*s1*s4, s2*s4*s2*s4, s2*s3*s2*s3*s2*s3*s2*s3, 
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1, s2*s3*s4*s3*s4*s3*s2*s3*s4*s3*s4*s3, 
s4*s3*s4*s3*s4*s3*s4*s3*s2*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s2*s3*s2 >; 
 

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