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Polytope of Type {2,20,12,2}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,20,12,2}*1920
if this polytope has a name.
Group : SmallGroup(1920,205047)
Rank : 5
Schlafli Type : {2,20,12,2}
Number of vertices, edges, etc : 2, 20, 120, 12, 2
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 : {2,10,12,2}*960, {2,20,6,2}*960a
   3-fold quotients : {2,20,4,2}*640
   4-fold quotients : {2,10,6,2}*480
   5-fold quotients : {2,4,12,2}*384a
   6-fold quotients : {2,20,2,2}*320, {2,10,4,2}*320
   10-fold quotients : {2,2,12,2}*192, {2,4,6,2}*192a
   12-fold quotients : {2,10,2,2}*160
   15-fold quotients : {2,4,4,2}*128
   20-fold quotients : {2,2,6,2}*96
   24-fold quotients : {2,5,2,2}*80
   30-fold quotients : {2,2,4,2}*64, {2,4,2,2}*64
   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 := (  4,  7)(  5,  6)(  9, 12)( 10, 11)( 14, 17)( 15, 16)( 19, 22)( 20, 21)
( 24, 27)( 25, 26)( 29, 32)( 30, 31)( 34, 37)( 35, 36)( 39, 42)( 40, 41)
( 44, 47)( 45, 46)( 49, 52)( 50, 51)( 54, 57)( 55, 56)( 59, 62)( 60, 61)
( 63, 93)( 64, 97)( 65, 96)( 66, 95)( 67, 94)( 68, 98)( 69,102)( 70,101)
( 71,100)( 72, 99)( 73,103)( 74,107)( 75,106)( 76,105)( 77,104)( 78,108)
( 79,112)( 80,111)( 81,110)( 82,109)( 83,113)( 84,117)( 85,116)( 86,115)
( 87,114)( 88,118)( 89,122)( 90,121)( 91,120)( 92,119);;
s2 := (  3, 64)(  4, 63)(  5, 67)(  6, 66)(  7, 65)(  8, 74)(  9, 73)( 10, 77)
( 11, 76)( 12, 75)( 13, 69)( 14, 68)( 15, 72)( 16, 71)( 17, 70)( 18, 79)
( 19, 78)( 20, 82)( 21, 81)( 22, 80)( 23, 89)( 24, 88)( 25, 92)( 26, 91)
( 27, 90)( 28, 84)( 29, 83)( 30, 87)( 31, 86)( 32, 85)( 33, 94)( 34, 93)
( 35, 97)( 36, 96)( 37, 95)( 38,104)( 39,103)( 40,107)( 41,106)( 42,105)
( 43, 99)( 44, 98)( 45,102)( 46,101)( 47,100)( 48,109)( 49,108)( 50,112)
( 51,111)( 52,110)( 53,119)( 54,118)( 55,122)( 56,121)( 57,120)( 58,114)
( 59,113)( 60,117)( 61,116)( 62,115);;
s3 := (  3,  8)(  4,  9)(  5, 10)(  6, 11)(  7, 12)( 18, 23)( 19, 24)( 20, 25)
( 21, 26)( 22, 27)( 33, 38)( 34, 39)( 35, 40)( 36, 41)( 37, 42)( 48, 53)
( 49, 54)( 50, 55)( 51, 56)( 52, 57)( 63, 83)( 64, 84)( 65, 85)( 66, 86)
( 67, 87)( 68, 78)( 69, 79)( 70, 80)( 71, 81)( 72, 82)( 73, 88)( 74, 89)
( 75, 90)( 76, 91)( 77, 92)( 93,113)( 94,114)( 95,115)( 96,116)( 97,117)
( 98,108)( 99,109)(100,110)(101,111)(102,112)(103,118)(104,119)(105,120)
(106,121)(107,122);;
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, s1*s2*s3*s2*s1*s2*s3*s2, 
s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3, 
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2 ];;
poly := F / rels;;
 
Permutation Representation (Magma) :
s0 := Sym(124)!(1,2);
s1 := Sym(124)!(  4,  7)(  5,  6)(  9, 12)( 10, 11)( 14, 17)( 15, 16)( 19, 22)
( 20, 21)( 24, 27)( 25, 26)( 29, 32)( 30, 31)( 34, 37)( 35, 36)( 39, 42)
( 40, 41)( 44, 47)( 45, 46)( 49, 52)( 50, 51)( 54, 57)( 55, 56)( 59, 62)
( 60, 61)( 63, 93)( 64, 97)( 65, 96)( 66, 95)( 67, 94)( 68, 98)( 69,102)
( 70,101)( 71,100)( 72, 99)( 73,103)( 74,107)( 75,106)( 76,105)( 77,104)
( 78,108)( 79,112)( 80,111)( 81,110)( 82,109)( 83,113)( 84,117)( 85,116)
( 86,115)( 87,114)( 88,118)( 89,122)( 90,121)( 91,120)( 92,119);
s2 := Sym(124)!(  3, 64)(  4, 63)(  5, 67)(  6, 66)(  7, 65)(  8, 74)(  9, 73)
( 10, 77)( 11, 76)( 12, 75)( 13, 69)( 14, 68)( 15, 72)( 16, 71)( 17, 70)
( 18, 79)( 19, 78)( 20, 82)( 21, 81)( 22, 80)( 23, 89)( 24, 88)( 25, 92)
( 26, 91)( 27, 90)( 28, 84)( 29, 83)( 30, 87)( 31, 86)( 32, 85)( 33, 94)
( 34, 93)( 35, 97)( 36, 96)( 37, 95)( 38,104)( 39,103)( 40,107)( 41,106)
( 42,105)( 43, 99)( 44, 98)( 45,102)( 46,101)( 47,100)( 48,109)( 49,108)
( 50,112)( 51,111)( 52,110)( 53,119)( 54,118)( 55,122)( 56,121)( 57,120)
( 58,114)( 59,113)( 60,117)( 61,116)( 62,115);
s3 := Sym(124)!(  3,  8)(  4,  9)(  5, 10)(  6, 11)(  7, 12)( 18, 23)( 19, 24)
( 20, 25)( 21, 26)( 22, 27)( 33, 38)( 34, 39)( 35, 40)( 36, 41)( 37, 42)
( 48, 53)( 49, 54)( 50, 55)( 51, 56)( 52, 57)( 63, 83)( 64, 84)( 65, 85)
( 66, 86)( 67, 87)( 68, 78)( 69, 79)( 70, 80)( 71, 81)( 72, 82)( 73, 88)
( 74, 89)( 75, 90)( 76, 91)( 77, 92)( 93,113)( 94,114)( 95,115)( 96,116)
( 97,117)( 98,108)( 99,109)(100,110)(101,111)(102,112)(103,118)(104,119)
(105,120)(106,121)(107,122);
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, 
s1*s2*s3*s2*s1*s2*s3*s2, s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3, 
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2 >; 
 

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