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

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {6,20,2,2}*1920a
if this polytope has a name.
Group : SmallGroup(1920,240407)
Rank : 5
Schlafli Type : {6,20,2,2}
Number of vertices, edges, etc : 12, 120, 40, 2, 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 : {6,20,2,2}*960b
   4-fold quotients : {6,10,2,2}*480
   5-fold quotients : {6,4,2,2}*384
   10-fold quotients : {3,4,2,2}*192, {6,4,2,2}*192b, {6,4,2,2}*192c
   12-fold quotients : {2,10,2,2}*160
   20-fold quotients : {3,4,2,2}*96, {6,2,2,2}*96
   24-fold quotients : {2,5,2,2}*80
   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 := (  2,  3)(  6,  7)( 10, 11)( 14, 15)( 18, 19)( 21, 41)( 22, 43)( 23, 42)
( 24, 44)( 25, 45)( 26, 47)( 27, 46)( 28, 48)( 29, 49)( 30, 51)( 31, 50)
( 32, 52)( 33, 53)( 34, 55)( 35, 54)( 36, 56)( 37, 57)( 38, 59)( 39, 58)
( 40, 60)( 62, 63)( 66, 67)( 70, 71)( 74, 75)( 78, 79)( 81,101)( 82,103)
( 83,102)( 84,104)( 85,105)( 86,107)( 87,106)( 88,108)( 89,109)( 90,111)
( 91,110)( 92,112)( 93,113)( 94,115)( 95,114)( 96,116)( 97,117)( 98,119)
( 99,118)(100,120);;
s1 := (  1, 21)(  2, 22)(  3, 24)(  4, 23)(  5, 37)(  6, 38)(  7, 40)(  8, 39)
(  9, 33)( 10, 34)( 11, 36)( 12, 35)( 13, 29)( 14, 30)( 15, 32)( 16, 31)
( 17, 25)( 18, 26)( 19, 28)( 20, 27)( 43, 44)( 45, 57)( 46, 58)( 47, 60)
( 48, 59)( 49, 53)( 50, 54)( 51, 56)( 52, 55)( 61, 81)( 62, 82)( 63, 84)
( 64, 83)( 65, 97)( 66, 98)( 67,100)( 68, 99)( 69, 93)( 70, 94)( 71, 96)
( 72, 95)( 73, 89)( 74, 90)( 75, 92)( 76, 91)( 77, 85)( 78, 86)( 79, 88)
( 80, 87)(103,104)(105,117)(106,118)(107,120)(108,119)(109,113)(110,114)
(111,116)(112,115);;
s2 := (  1, 68)(  2, 67)(  3, 66)(  4, 65)(  5, 64)(  6, 63)(  7, 62)(  8, 61)
(  9, 80)( 10, 79)( 11, 78)( 12, 77)( 13, 76)( 14, 75)( 15, 74)( 16, 73)
( 17, 72)( 18, 71)( 19, 70)( 20, 69)( 21, 88)( 22, 87)( 23, 86)( 24, 85)
( 25, 84)( 26, 83)( 27, 82)( 28, 81)( 29,100)( 30, 99)( 31, 98)( 32, 97)
( 33, 96)( 34, 95)( 35, 94)( 36, 93)( 37, 92)( 38, 91)( 39, 90)( 40, 89)
( 41,108)( 42,107)( 43,106)( 44,105)( 45,104)( 46,103)( 47,102)( 48,101)
( 49,120)( 50,119)( 51,118)( 52,117)( 53,116)( 54,115)( 55,114)( 56,113)
( 57,112)( 58,111)( 59,110)( 60,109);;
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*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1, 
s2*s0*s1*s2*s0*s1*s0*s1*s2*s0*s1*s2*s0*s1*s0*s1, 
s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1, 
s2*s0*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s0*s1*s2*s0*s1*s2*s1*s2*s0*s1 ];;
poly := F / rels;;

Permutation Representation (Magma) :

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

to this polytope