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

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,40,6,2}*1920
if this polytope has a name.
Group : SmallGroup(1920,235349)
Rank : 5
Schlafli Type : {2,40,6,2}
Number of vertices, edges, etc : 2, 40, 120, 6, 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 : {2,20,6,2}*960a
   3-fold quotients : {2,40,2,2}*640
   4-fold quotients : {2,10,6,2}*480
   5-fold quotients : {2,8,6,2}*384
   6-fold quotients : {2,20,2,2}*320
   10-fold quotients : {2,4,6,2}*192a
   12-fold quotients : {2,10,2,2}*160
   15-fold quotients : {2,8,2,2}*128
   20-fold quotients : {2,2,6,2}*96
   24-fold quotients : {2,5,2,2}*80
   30-fold quotients : {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)( 33, 48)( 34, 52)( 35, 51)( 36, 50)
( 37, 49)( 38, 53)( 39, 57)( 40, 56)( 41, 55)( 42, 54)( 43, 58)( 44, 62)
( 45, 61)( 46, 60)( 47, 59)( 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)( 33,109)( 34,108)
( 35,112)( 36,111)( 37,110)( 38,119)( 39,118)( 40,122)( 41,121)( 42,120)
( 43,114)( 44,113)( 45,117)( 46,116)( 47,115)( 48, 94)( 49, 93)( 50, 97)
( 51, 96)( 52, 95)( 53,104)( 54,103)( 55,107)( 56,106)( 57,105)( 58, 99)
( 59, 98)( 60,102)( 61,101)( 62,100);;
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, 68)( 64, 69)( 65, 70)( 66, 71)
( 67, 72)( 78, 83)( 79, 84)( 80, 85)( 81, 86)( 82, 87)( 93, 98)( 94, 99)
( 95,100)( 96,101)( 97,102)(108,113)(109,114)(110,115)(111,116)(112,117);;
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, 
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)!(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)( 33, 48)( 34, 52)( 35, 51)
( 36, 50)( 37, 49)( 38, 53)( 39, 57)( 40, 56)( 41, 55)( 42, 54)( 43, 58)
( 44, 62)( 45, 61)( 46, 60)( 47, 59)( 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)( 33,109)
( 34,108)( 35,112)( 36,111)( 37,110)( 38,119)( 39,118)( 40,122)( 41,121)
( 42,120)( 43,114)( 44,113)( 45,117)( 46,116)( 47,115)( 48, 94)( 49, 93)
( 50, 97)( 51, 96)( 52, 95)( 53,104)( 54,103)( 55,107)( 56,106)( 57,105)
( 58, 99)( 59, 98)( 60,102)( 61,101)( 62,100);
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, 68)( 64, 69)( 65, 70)
( 66, 71)( 67, 72)( 78, 83)( 79, 84)( 80, 85)( 81, 86)( 82, 87)( 93, 98)
( 94, 99)( 95,100)( 96,101)( 97,102)(108,113)(109,114)(110,115)(111,116)
(112,117);
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, 
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