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

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,2,6,40}*1920
if this polytope has a name.
Group : SmallGroup(1920,235349)
Rank : 5
Schlafli Type : {2,2,6,40}
Number of vertices, edges, etc : 2, 2, 6, 120, 40
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 : {2,2,6,20}*960a
   3-fold quotients : {2,2,2,40}*640
   4-fold quotients : {2,2,6,10}*480
   5-fold quotients : {2,2,6,8}*384
   6-fold quotients : {2,2,2,20}*320
   10-fold quotients : {2,2,6,4}*192a
   12-fold quotients : {2,2,2,10}*160
   15-fold quotients : {2,2,2,8}*128
   20-fold quotients : {2,2,6,2}*96
   24-fold quotients : {2,2,2,5}*80
   30-fold quotients : {2,2,2,4}*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 := (3,4);;
s2 := ( 10, 15)( 11, 16)( 12, 17)( 13, 18)( 14, 19)( 25, 30)( 26, 31)( 27, 32)
( 28, 33)( 29, 34)( 40, 45)( 41, 46)( 42, 47)( 43, 48)( 44, 49)( 55, 60)
( 56, 61)( 57, 62)( 58, 63)( 59, 64)( 70, 75)( 71, 76)( 72, 77)( 73, 78)
( 74, 79)( 85, 90)( 86, 91)( 87, 92)( 88, 93)( 89, 94)(100,105)(101,106)
(102,107)(103,108)(104,109)(115,120)(116,121)(117,122)(118,123)(119,124);;
s3 := (  5, 10)(  6, 14)(  7, 13)(  8, 12)(  9, 11)( 16, 19)( 17, 18)( 20, 25)
( 21, 29)( 22, 28)( 23, 27)( 24, 26)( 31, 34)( 32, 33)( 35, 55)( 36, 59)
( 37, 58)( 38, 57)( 39, 56)( 40, 50)( 41, 54)( 42, 53)( 43, 52)( 44, 51)
( 45, 60)( 46, 64)( 47, 63)( 48, 62)( 49, 61)( 65,100)( 66,104)( 67,103)
( 68,102)( 69,101)( 70, 95)( 71, 99)( 72, 98)( 73, 97)( 74, 96)( 75,105)
( 76,109)( 77,108)( 78,107)( 79,106)( 80,115)( 81,119)( 82,118)( 83,117)
( 84,116)( 85,110)( 86,114)( 87,113)( 88,112)( 89,111)( 90,120)( 91,124)
( 92,123)( 93,122)( 94,121);;
s4 := (  5, 66)(  6, 65)(  7, 69)(  8, 68)(  9, 67)( 10, 71)( 11, 70)( 12, 74)
( 13, 73)( 14, 72)( 15, 76)( 16, 75)( 17, 79)( 18, 78)( 19, 77)( 20, 81)
( 21, 80)( 22, 84)( 23, 83)( 24, 82)( 25, 86)( 26, 85)( 27, 89)( 28, 88)
( 29, 87)( 30, 91)( 31, 90)( 32, 94)( 33, 93)( 34, 92)( 35,111)( 36,110)
( 37,114)( 38,113)( 39,112)( 40,116)( 41,115)( 42,119)( 43,118)( 44,117)
( 45,121)( 46,120)( 47,124)( 48,123)( 49,122)( 50, 96)( 51, 95)( 52, 99)
( 53, 98)( 54, 97)( 55,101)( 56,100)( 57,104)( 58,103)( 59,102)( 60,106)
( 61,105)( 62,109)( 63,108)( 64,107);;
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, s1*s2*s1*s2, s0*s3*s0*s3, 
s1*s3*s1*s3, s0*s4*s0*s4, s1*s4*s1*s4, 
s2*s4*s2*s4, s2*s3*s4*s3*s2*s3*s4*s3, 
s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3, 
s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4 ];;
poly := F / rels;;

Permutation Representation (Magma) :

s0 := Sym(124)!(1,2);
s1 := Sym(124)!(3,4);
s2 := Sym(124)!( 10, 15)( 11, 16)( 12, 17)( 13, 18)( 14, 19)( 25, 30)( 26, 31)
( 27, 32)( 28, 33)( 29, 34)( 40, 45)( 41, 46)( 42, 47)( 43, 48)( 44, 49)
( 55, 60)( 56, 61)( 57, 62)( 58, 63)( 59, 64)( 70, 75)( 71, 76)( 72, 77)
( 73, 78)( 74, 79)( 85, 90)( 86, 91)( 87, 92)( 88, 93)( 89, 94)(100,105)
(101,106)(102,107)(103,108)(104,109)(115,120)(116,121)(117,122)(118,123)
(119,124);
s3 := Sym(124)!(  5, 10)(  6, 14)(  7, 13)(  8, 12)(  9, 11)( 16, 19)( 17, 18)
( 20, 25)( 21, 29)( 22, 28)( 23, 27)( 24, 26)( 31, 34)( 32, 33)( 35, 55)
( 36, 59)( 37, 58)( 38, 57)( 39, 56)( 40, 50)( 41, 54)( 42, 53)( 43, 52)
( 44, 51)( 45, 60)( 46, 64)( 47, 63)( 48, 62)( 49, 61)( 65,100)( 66,104)
( 67,103)( 68,102)( 69,101)( 70, 95)( 71, 99)( 72, 98)( 73, 97)( 74, 96)
( 75,105)( 76,109)( 77,108)( 78,107)( 79,106)( 80,115)( 81,119)( 82,118)
( 83,117)( 84,116)( 85,110)( 86,114)( 87,113)( 88,112)( 89,111)( 90,120)
( 91,124)( 92,123)( 93,122)( 94,121);
s4 := Sym(124)!(  5, 66)(  6, 65)(  7, 69)(  8, 68)(  9, 67)( 10, 71)( 11, 70)
( 12, 74)( 13, 73)( 14, 72)( 15, 76)( 16, 75)( 17, 79)( 18, 78)( 19, 77)
( 20, 81)( 21, 80)( 22, 84)( 23, 83)( 24, 82)( 25, 86)( 26, 85)( 27, 89)
( 28, 88)( 29, 87)( 30, 91)( 31, 90)( 32, 94)( 33, 93)( 34, 92)( 35,111)
( 36,110)( 37,114)( 38,113)( 39,112)( 40,116)( 41,115)( 42,119)( 43,118)
( 44,117)( 45,121)( 46,120)( 47,124)( 48,123)( 49,122)( 50, 96)( 51, 95)
( 52, 99)( 53, 98)( 54, 97)( 55,101)( 56,100)( 57,104)( 58,103)( 59,102)
( 60,106)( 61,105)( 62,109)( 63,108)( 64,107);
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, 
s1*s2*s1*s2, s0*s3*s0*s3, s1*s3*s1*s3, 
s0*s4*s0*s4, s1*s4*s1*s4, s2*s4*s2*s4, 
s2*s3*s4*s3*s2*s3*s4*s3, s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3, 
s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4 >;

to this polytope