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Polytope of Type {2,20,6,2}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,20,6,2}*1920a
if this polytope has a name.
Group : SmallGroup(1920,240407)
Rank : 5
Schlafli Type : {2,20,6,2}
Number of vertices, edges, etc : 2, 40, 120, 12, 2
Order of s0s1s2s3s4 : 30
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 : {2,20,6,2}*960b
   4-fold quotients : {2,10,6,2}*480
   5-fold quotients : {2,4,6,2}*384
   10-fold quotients : {2,4,3,2}*192, {2,4,6,2}*192b, {2,4,6,2}*192c
   12-fold quotients : {2,10,2,2}*160
   20-fold quotients : {2,4,3,2}*96, {2,2,6,2}*96
   24-fold quotients : {2,5,2,2}*80
   40-fold quotients : {2,2,3,2}*48
   60-fold quotients : {2,2,2,2}*32
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :
s0 := (1,2);;
s1 := (  3,  5)(  4,  6)(  7, 21)(  8, 22)(  9, 19)( 10, 20)( 11, 17)( 12, 18)
( 13, 15)( 14, 16)( 23, 25)( 24, 26)( 27, 41)( 28, 42)( 29, 39)( 30, 40)
( 31, 37)( 32, 38)( 33, 35)( 34, 36)( 43, 45)( 44, 46)( 47, 61)( 48, 62)
( 49, 59)( 50, 60)( 51, 57)( 52, 58)( 53, 55)( 54, 56)( 63, 65)( 64, 66)
( 67, 81)( 68, 82)( 69, 79)( 70, 80)( 71, 77)( 72, 78)( 73, 75)( 74, 76)
( 83, 85)( 84, 86)( 87,101)( 88,102)( 89, 99)( 90,100)( 91, 97)( 92, 98)
( 93, 95)( 94, 96)(103,105)(104,106)(107,121)(108,122)(109,119)(110,120)
(111,117)(112,118)(113,115)(114,116);;
s2 := (  3,  7)(  4,  9)(  5,  8)(  6, 10)( 11, 19)( 12, 21)( 13, 20)( 14, 22)
( 16, 17)( 23, 47)( 24, 49)( 25, 48)( 26, 50)( 27, 43)( 28, 45)( 29, 44)
( 30, 46)( 31, 59)( 32, 61)( 33, 60)( 34, 62)( 35, 55)( 36, 57)( 37, 56)
( 38, 58)( 39, 51)( 40, 53)( 41, 52)( 42, 54)( 63, 67)( 64, 69)( 65, 68)
( 66, 70)( 71, 79)( 72, 81)( 73, 80)( 74, 82)( 76, 77)( 83,107)( 84,109)
( 85,108)( 86,110)( 87,103)( 88,105)( 89,104)( 90,106)( 91,119)( 92,121)
( 93,120)( 94,122)( 95,115)( 96,117)( 97,116)( 98,118)( 99,111)(100,113)
(101,112)(102,114);;
s3 := (  3,103)(  4,106)(  5,105)(  6,104)(  7,107)(  8,110)(  9,109)( 10,108)
( 11,111)( 12,114)( 13,113)( 14,112)( 15,115)( 16,118)( 17,117)( 18,116)
( 19,119)( 20,122)( 21,121)( 22,120)( 23, 83)( 24, 86)( 25, 85)( 26, 84)
( 27, 87)( 28, 90)( 29, 89)( 30, 88)( 31, 91)( 32, 94)( 33, 93)( 34, 92)
( 35, 95)( 36, 98)( 37, 97)( 38, 96)( 39, 99)( 40,102)( 41,101)( 42,100)
( 43, 63)( 44, 66)( 45, 65)( 46, 64)( 47, 67)( 48, 70)( 49, 69)( 50, 68)
( 51, 71)( 52, 74)( 53, 73)( 54, 72)( 55, 75)( 56, 78)( 57, 77)( 58, 76)
( 59, 79)( 60, 82)( 61, 81)( 62, 80);;
s4 := (123,124);;
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*s1*s0*s1, 
s0*s2*s0*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, s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3, 
s3*s1*s2*s3*s2*s3*s1*s2*s3*s1*s2*s3*s2*s3*s1*s2, 
s1*s2*s3*s2*s1*s2*s1*s2*s1*s2*s3*s2*s1*s2*s1*s2, 
s3*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s3*s1*s2*s1*s2*s3*s1*s2*s3*s1*s2*s1*s2 ];;
poly := F / rels;;
 
Permutation Representation (Magma) :
s0 := Sym(124)!(1,2);
s1 := Sym(124)!(  3,  5)(  4,  6)(  7, 21)(  8, 22)(  9, 19)( 10, 20)( 11, 17)
( 12, 18)( 13, 15)( 14, 16)( 23, 25)( 24, 26)( 27, 41)( 28, 42)( 29, 39)
( 30, 40)( 31, 37)( 32, 38)( 33, 35)( 34, 36)( 43, 45)( 44, 46)( 47, 61)
( 48, 62)( 49, 59)( 50, 60)( 51, 57)( 52, 58)( 53, 55)( 54, 56)( 63, 65)
( 64, 66)( 67, 81)( 68, 82)( 69, 79)( 70, 80)( 71, 77)( 72, 78)( 73, 75)
( 74, 76)( 83, 85)( 84, 86)( 87,101)( 88,102)( 89, 99)( 90,100)( 91, 97)
( 92, 98)( 93, 95)( 94, 96)(103,105)(104,106)(107,121)(108,122)(109,119)
(110,120)(111,117)(112,118)(113,115)(114,116);
s2 := Sym(124)!(  3,  7)(  4,  9)(  5,  8)(  6, 10)( 11, 19)( 12, 21)( 13, 20)
( 14, 22)( 16, 17)( 23, 47)( 24, 49)( 25, 48)( 26, 50)( 27, 43)( 28, 45)
( 29, 44)( 30, 46)( 31, 59)( 32, 61)( 33, 60)( 34, 62)( 35, 55)( 36, 57)
( 37, 56)( 38, 58)( 39, 51)( 40, 53)( 41, 52)( 42, 54)( 63, 67)( 64, 69)
( 65, 68)( 66, 70)( 71, 79)( 72, 81)( 73, 80)( 74, 82)( 76, 77)( 83,107)
( 84,109)( 85,108)( 86,110)( 87,103)( 88,105)( 89,104)( 90,106)( 91,119)
( 92,121)( 93,120)( 94,122)( 95,115)( 96,117)( 97,116)( 98,118)( 99,111)
(100,113)(101,112)(102,114);
s3 := Sym(124)!(  3,103)(  4,106)(  5,105)(  6,104)(  7,107)(  8,110)(  9,109)
( 10,108)( 11,111)( 12,114)( 13,113)( 14,112)( 15,115)( 16,118)( 17,117)
( 18,116)( 19,119)( 20,122)( 21,121)( 22,120)( 23, 83)( 24, 86)( 25, 85)
( 26, 84)( 27, 87)( 28, 90)( 29, 89)( 30, 88)( 31, 91)( 32, 94)( 33, 93)
( 34, 92)( 35, 95)( 36, 98)( 37, 97)( 38, 96)( 39, 99)( 40,102)( 41,101)
( 42,100)( 43, 63)( 44, 66)( 45, 65)( 46, 64)( 47, 67)( 48, 70)( 49, 69)
( 50, 68)( 51, 71)( 52, 74)( 53, 73)( 54, 72)( 55, 75)( 56, 78)( 57, 77)
( 58, 76)( 59, 79)( 60, 82)( 61, 81)( 62, 80);
s4 := Sym(124)!(123,124);
poly := sub<Sym(124)|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*s1*s0*s1, s0*s2*s0*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, 
s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3, 
s3*s1*s2*s3*s2*s3*s1*s2*s3*s1*s2*s3*s2*s3*s1*s2, 
s1*s2*s3*s2*s1*s2*s1*s2*s1*s2*s3*s2*s1*s2*s1*s2, 
s3*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s3*s1*s2*s1*s2*s3*s1*s2*s3*s1*s2*s1*s2 >; 
 

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