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Polytope of Type {5,2,12,4}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {5,2,12,4}*1920b
if this polytope has a name.
Group : SmallGroup(1920,240141)
Rank : 5
Schlafli Type : {5,2,12,4}
Number of vertices, edges, etc : 5, 5, 24, 48, 8
Order of s0s1s2s3s4 : 60
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 : {5,2,12,4}*960b, {5,2,12,4}*960c, {5,2,6,4}*960
   4-fold quotients : {5,2,12,2}*480, {5,2,3,4}*480, {5,2,6,4}*480b, {5,2,6,4}*480c
   8-fold quotients : {5,2,3,4}*240, {5,2,6,2}*240
   12-fold quotients : {5,2,4,2}*160
   16-fold quotients : {5,2,3,2}*120
   24-fold quotients : {5,2,2,2}*80
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :
s0 := (2,3)(4,5);;
s1 := (1,2)(3,4);;
s2 := (  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)( 55, 56)( 58, 62)
( 59, 64)( 60, 63)( 61, 65)( 67, 68)( 70, 74)( 71, 76)( 72, 75)( 73, 77)
( 78, 90)( 79, 92)( 80, 91)( 81, 93)( 82, 98)( 83,100)( 84, 99)( 85,101)
( 86, 94)( 87, 96)( 88, 95)( 89, 97);;
s3 := (  6, 34)(  7, 35)(  8, 37)(  9, 36)( 10, 30)( 11, 31)( 12, 33)( 13, 32)
( 14, 38)( 15, 39)( 16, 41)( 17, 40)( 18, 46)( 19, 47)( 20, 49)( 21, 48)
( 22, 42)( 23, 43)( 24, 45)( 25, 44)( 26, 50)( 27, 51)( 28, 53)( 29, 52)
( 54, 82)( 55, 83)( 56, 85)( 57, 84)( 58, 78)( 59, 79)( 60, 81)( 61, 80)
( 62, 86)( 63, 87)( 64, 89)( 65, 88)( 66, 94)( 67, 95)( 68, 97)( 69, 96)
( 70, 90)( 71, 91)( 72, 93)( 73, 92)( 74, 98)( 75, 99)( 76,101)( 77,100);;
s4 := (  6, 57)(  7, 56)(  8, 55)(  9, 54)( 10, 61)( 11, 60)( 12, 59)( 13, 58)
( 14, 65)( 15, 64)( 16, 63)( 17, 62)( 18, 69)( 19, 68)( 20, 67)( 21, 66)
( 22, 73)( 23, 72)( 24, 71)( 25, 70)( 26, 77)( 27, 76)( 28, 75)( 29, 74)
( 30, 81)( 31, 80)( 32, 79)( 33, 78)( 34, 85)( 35, 84)( 36, 83)( 37, 82)
( 38, 89)( 39, 88)( 40, 87)( 41, 86)( 42, 93)( 43, 92)( 44, 91)( 45, 90)
( 46, 97)( 47, 96)( 48, 95)( 49, 94)( 50,101)( 51,100)( 52, 99)( 53, 98);;
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, 
s3*s4*s3*s4*s3*s4*s3*s4, s0*s1*s0*s1*s0*s1*s0*s1*s0*s1, 
s2*s3*s4*s3*s2*s3*s2*s3*s4*s3*s2*s3, 
s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3 ];;
poly := F / rels;;
 
Permutation Representation (Magma) :
s0 := Sym(101)!(2,3)(4,5);
s1 := Sym(101)!(1,2)(3,4);
s2 := 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)( 55, 56)
( 58, 62)( 59, 64)( 60, 63)( 61, 65)( 67, 68)( 70, 74)( 71, 76)( 72, 75)
( 73, 77)( 78, 90)( 79, 92)( 80, 91)( 81, 93)( 82, 98)( 83,100)( 84, 99)
( 85,101)( 86, 94)( 87, 96)( 88, 95)( 89, 97);
s3 := Sym(101)!(  6, 34)(  7, 35)(  8, 37)(  9, 36)( 10, 30)( 11, 31)( 12, 33)
( 13, 32)( 14, 38)( 15, 39)( 16, 41)( 17, 40)( 18, 46)( 19, 47)( 20, 49)
( 21, 48)( 22, 42)( 23, 43)( 24, 45)( 25, 44)( 26, 50)( 27, 51)( 28, 53)
( 29, 52)( 54, 82)( 55, 83)( 56, 85)( 57, 84)( 58, 78)( 59, 79)( 60, 81)
( 61, 80)( 62, 86)( 63, 87)( 64, 89)( 65, 88)( 66, 94)( 67, 95)( 68, 97)
( 69, 96)( 70, 90)( 71, 91)( 72, 93)( 73, 92)( 74, 98)( 75, 99)( 76,101)
( 77,100);
s4 := Sym(101)!(  6, 57)(  7, 56)(  8, 55)(  9, 54)( 10, 61)( 11, 60)( 12, 59)
( 13, 58)( 14, 65)( 15, 64)( 16, 63)( 17, 62)( 18, 69)( 19, 68)( 20, 67)
( 21, 66)( 22, 73)( 23, 72)( 24, 71)( 25, 70)( 26, 77)( 27, 76)( 28, 75)
( 29, 74)( 30, 81)( 31, 80)( 32, 79)( 33, 78)( 34, 85)( 35, 84)( 36, 83)
( 37, 82)( 38, 89)( 39, 88)( 40, 87)( 41, 86)( 42, 93)( 43, 92)( 44, 91)
( 45, 90)( 46, 97)( 47, 96)( 48, 95)( 49, 94)( 50,101)( 51,100)( 52, 99)
( 53, 98);
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, s3*s4*s3*s4*s3*s4*s3*s4, 
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1, s2*s3*s4*s3*s2*s3*s2*s3*s4*s3*s2*s3, 
s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3 >; 
 

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