Polytope of Type {6,40,2,2}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {6,40,2,2}*1920
if this polytope has a name.
Group : SmallGroup(1920,235349)
Rank : 5
Schlafli Type : {6,40,2,2}
Number of vertices, edges, etc : 6, 120, 40, 2, 2
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 : {6,20,2,2}*960a
   3-fold quotients : {2,40,2,2}*640
   4-fold quotients : {6,10,2,2}*480
   5-fold quotients : {6,8,2,2}*384
   6-fold quotients : {2,20,2,2}*320
   10-fold quotients : {6,4,2,2}*192a
   12-fold quotients : {2,10,2,2}*160
   15-fold quotients : {2,8,2,2}*128
   20-fold quotients : {6,2,2,2}*96
   24-fold quotients : {2,5,2,2}*80
   30-fold quotients : {2,4,2,2}*64
   40-fold quotients : {3,2,2,2}*48
   60-fold quotients : {2,2,2,2}*32
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :

s0 := (  6, 11)(  7, 12)(  8, 13)(  9, 14)( 10, 15)( 21, 26)( 22, 27)( 23, 28)
( 24, 29)( 25, 30)( 36, 41)( 37, 42)( 38, 43)( 39, 44)( 40, 45)( 51, 56)
( 52, 57)( 53, 58)( 54, 59)( 55, 60)( 66, 71)( 67, 72)( 68, 73)( 69, 74)
( 70, 75)( 81, 86)( 82, 87)( 83, 88)( 84, 89)( 85, 90)( 96,101)( 97,102)
( 98,103)( 99,104)(100,105)(111,116)(112,117)(113,118)(114,119)(115,120);;
s1 := (  1,  6)(  2, 10)(  3,  9)(  4,  8)(  5,  7)( 12, 15)( 13, 14)( 16, 21)
( 17, 25)( 18, 24)( 19, 23)( 20, 22)( 27, 30)( 28, 29)( 31, 51)( 32, 55)
( 33, 54)( 34, 53)( 35, 52)( 36, 46)( 37, 50)( 38, 49)( 39, 48)( 40, 47)
( 41, 56)( 42, 60)( 43, 59)( 44, 58)( 45, 57)( 61, 96)( 62,100)( 63, 99)
( 64, 98)( 65, 97)( 66, 91)( 67, 95)( 68, 94)( 69, 93)( 70, 92)( 71,101)
( 72,105)( 73,104)( 74,103)( 75,102)( 76,111)( 77,115)( 78,114)( 79,113)
( 80,112)( 81,106)( 82,110)( 83,109)( 84,108)( 85,107)( 86,116)( 87,120)
( 88,119)( 89,118)( 90,117);;
s2 := (  1, 62)(  2, 61)(  3, 65)(  4, 64)(  5, 63)(  6, 67)(  7, 66)(  8, 70)
(  9, 69)( 10, 68)( 11, 72)( 12, 71)( 13, 75)( 14, 74)( 15, 73)( 16, 77)
( 17, 76)( 18, 80)( 19, 79)( 20, 78)( 21, 82)( 22, 81)( 23, 85)( 24, 84)
( 25, 83)( 26, 87)( 27, 86)( 28, 90)( 29, 89)( 30, 88)( 31,107)( 32,106)
( 33,110)( 34,109)( 35,108)( 36,112)( 37,111)( 38,115)( 39,114)( 40,113)
( 41,117)( 42,116)( 43,120)( 44,119)( 45,118)( 46, 92)( 47, 91)( 48, 95)
( 49, 94)( 50, 93)( 51, 97)( 52, 96)( 53,100)( 54, 99)( 55, 98)( 56,102)
( 57,101)( 58,105)( 59,104)( 60,103);;
s3 := (121,122);;
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*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, 
s3*s4*s3*s4, s0*s1*s2*s1*s0*s1*s2*s1, 
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1, 
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*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)!(  6, 11)(  7, 12)(  8, 13)(  9, 14)( 10, 15)( 21, 26)( 22, 27)
( 23, 28)( 24, 29)( 25, 30)( 36, 41)( 37, 42)( 38, 43)( 39, 44)( 40, 45)
( 51, 56)( 52, 57)( 53, 58)( 54, 59)( 55, 60)( 66, 71)( 67, 72)( 68, 73)
( 69, 74)( 70, 75)( 81, 86)( 82, 87)( 83, 88)( 84, 89)( 85, 90)( 96,101)
( 97,102)( 98,103)( 99,104)(100,105)(111,116)(112,117)(113,118)(114,119)
(115,120);
s1 := Sym(124)!(  1,  6)(  2, 10)(  3,  9)(  4,  8)(  5,  7)( 12, 15)( 13, 14)
( 16, 21)( 17, 25)( 18, 24)( 19, 23)( 20, 22)( 27, 30)( 28, 29)( 31, 51)
( 32, 55)( 33, 54)( 34, 53)( 35, 52)( 36, 46)( 37, 50)( 38, 49)( 39, 48)
( 40, 47)( 41, 56)( 42, 60)( 43, 59)( 44, 58)( 45, 57)( 61, 96)( 62,100)
( 63, 99)( 64, 98)( 65, 97)( 66, 91)( 67, 95)( 68, 94)( 69, 93)( 70, 92)
( 71,101)( 72,105)( 73,104)( 74,103)( 75,102)( 76,111)( 77,115)( 78,114)
( 79,113)( 80,112)( 81,106)( 82,110)( 83,109)( 84,108)( 85,107)( 86,116)
( 87,120)( 88,119)( 89,118)( 90,117);
s2 := Sym(124)!(  1, 62)(  2, 61)(  3, 65)(  4, 64)(  5, 63)(  6, 67)(  7, 66)
(  8, 70)(  9, 69)( 10, 68)( 11, 72)( 12, 71)( 13, 75)( 14, 74)( 15, 73)
( 16, 77)( 17, 76)( 18, 80)( 19, 79)( 20, 78)( 21, 82)( 22, 81)( 23, 85)
( 24, 84)( 25, 83)( 26, 87)( 27, 86)( 28, 90)( 29, 89)( 30, 88)( 31,107)
( 32,106)( 33,110)( 34,109)( 35,108)( 36,112)( 37,111)( 38,115)( 39,114)
( 40,113)( 41,117)( 42,116)( 43,120)( 44,119)( 45,118)( 46, 92)( 47, 91)
( 48, 95)( 49, 94)( 50, 93)( 51, 97)( 52, 96)( 53,100)( 54, 99)( 55, 98)
( 56,102)( 57,101)( 58,105)( 59,104)( 60,103);
s3 := Sym(124)!(121,122);
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*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, s3*s4*s3*s4, 
s0*s1*s2*s1*s0*s1*s2*s1, s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1, 
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*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 >;

to this polytope