Polytope of Type {6,40}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {6,40}*480
Also Known As : {6,40|2}. if this polytope has another name.
Group : SmallGroup(480,328)
Rank : 3
Schlafli Type : {6,40}
Number of vertices, edges, etc : 6, 120, 40
Order of s₀s₁s₂ : 120
Order of s₀s₁s₂s₁ : 2
Special Properties :
   Compact Hyperbolic Quotient
   Locally Spherical
   Orientable
   Flat
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   {6,40,2} of size 960
   {6,40,4} of size 1920
   {6,40,4} of size 1920
Vertex Figure Of :
   {2,6,40} of size 960
   {3,6,40} of size 1440
   {4,6,40} of size 1920
   {3,6,40} of size 1920
   {4,6,40} of size 1920
Quotients (Maximal Quotients in Boldface) :
   2-fold quotients : {6,20}*240a
   3-fold quotients : {2,40}*160
   4-fold quotients : {6,10}*120
   5-fold quotients : {6,8}*96
   6-fold quotients : {2,20}*80
   10-fold quotients : {6,4}*48a
   12-fold quotients : {2,10}*40
   15-fold quotients : {2,8}*32
   20-fold quotients : {6,2}*24
   24-fold quotients : {2,5}*20
   30-fold quotients : {2,4}*16
   40-fold quotients : {3,2}*12
   60-fold quotients : {2,2}*8
Covers (Minimal Covers in Boldface) :
   2-fold covers : {6,80}*960, {12,40}*960a
   3-fold covers : {18,40}*1440, {6,120}*1440a, {6,120}*1440b
   4-fold covers : {12,40}*1920a, {24,40}*1920a, {24,40}*1920c, {12,80}*1920a, {12,80}*1920b, {6,160}*1920, {6,40}*1920d
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);;
poly := Group([s0,s1,s2]);;

Finitely Presented Group Representation (GAP) :

F := FreeGroup("s0","s1","s2");;
s0 := F.1;;  s1 := F.2;;  s2 := F.3;;  
rels := [ s0*s0, s1*s1, s2*s2, s0*s2*s0*s2, 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(120)!(  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(120)!(  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(120)!(  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);
poly := sub<Sym(120)|s0,s1,s2>;

Finitely Presented Group Representation (Magma) :

poly<s0,s1,s2> := Group< s0,s1,s2 | s0*s0, s1*s1, s2*s2, 
s0*s2*s0*s2, 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 >;

References : None.
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