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Polytope of Type {40,6}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {40,6}*480
Also Known As : {40,6|2}. if this polytope has another name.
Group : SmallGroup(480,328)
Rank : 3
Schlafli Type : {40,6}
Number of vertices, edges, etc : 40, 120, 6
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 :
   {40,6,2} of size 960
   {40,6,3} of size 1440
   {40,6,4} of size 1920
   {40,6,3} of size 1920
   {40,6,4} of size 1920
Vertex Figure Of :
   {2,40,6} of size 960
   {4,40,6} of size 1920
   {4,40,6} of size 1920
Quotients (Maximal Quotients in Boldface) :
   2-fold quotients : {20,6}*240a
   3-fold quotients : {40,2}*160
   4-fold quotients : {10,6}*120
   5-fold quotients : {8,6}*96
   6-fold quotients : {20,2}*80
   10-fold quotients : {4,6}*48a
   12-fold quotients : {10,2}*40
   15-fold quotients : {8,2}*32
   20-fold quotients : {2,6}*24
   24-fold quotients : {5,2}*20
   30-fold quotients : {4,2}*16
   40-fold quotients : {2,3}*12
   60-fold quotients : {2,2}*8
Covers (Minimal Covers in Boldface) :
   2-fold covers : {80,6}*960, {40,12}*960a
   3-fold covers : {40,18}*1440, {120,6}*1440a, {120,6}*1440b
   4-fold covers : {40,12}*1920a, {40,24}*1920a, {40,24}*1920c, {80,12}*1920a, {80,12}*1920b, {160,6}*1920, {40,6}*1920d
Permutation Representation (GAP) :
s0 := (  2,  5)(  3,  4)(  7, 10)(  8,  9)( 12, 15)( 13, 14)( 17, 20)( 18, 19)
( 22, 25)( 23, 24)( 27, 30)( 28, 29)( 31, 46)( 32, 50)( 33, 49)( 34, 48)
( 35, 47)( 36, 51)( 37, 55)( 38, 54)( 39, 53)( 40, 52)( 41, 56)( 42, 60)
( 43, 59)( 44, 58)( 45, 57)( 61, 91)( 62, 95)( 63, 94)( 64, 93)( 65, 92)
( 66, 96)( 67,100)( 68, 99)( 69, 98)( 70, 97)( 71,101)( 72,105)( 73,104)
( 74,103)( 75,102)( 76,106)( 77,110)( 78,109)( 79,108)( 80,107)( 81,111)
( 82,115)( 83,114)( 84,113)( 85,112)( 86,116)( 87,120)( 88,119)( 89,118)
( 90,117);;
s1 := (  1, 62)(  2, 61)(  3, 65)(  4, 64)(  5, 63)(  6, 72)(  7, 71)(  8, 75)
(  9, 74)( 10, 73)( 11, 67)( 12, 66)( 13, 70)( 14, 69)( 15, 68)( 16, 77)
( 17, 76)( 18, 80)( 19, 79)( 20, 78)( 21, 87)( 22, 86)( 23, 90)( 24, 89)
( 25, 88)( 26, 82)( 27, 81)( 28, 85)( 29, 84)( 30, 83)( 31,107)( 32,106)
( 33,110)( 34,109)( 35,108)( 36,117)( 37,116)( 38,120)( 39,119)( 40,118)
( 41,112)( 42,111)( 43,115)( 44,114)( 45,113)( 46, 92)( 47, 91)( 48, 95)
( 49, 94)( 50, 93)( 51,102)( 52,101)( 53,105)( 54,104)( 55,103)( 56, 97)
( 57, 96)( 58,100)( 59, 99)( 60, 98);;
s2 := (  1,  6)(  2,  7)(  3,  8)(  4,  9)(  5, 10)( 16, 21)( 17, 22)( 18, 23)
( 19, 24)( 20, 25)( 31, 36)( 32, 37)( 33, 38)( 34, 39)( 35, 40)( 46, 51)
( 47, 52)( 48, 53)( 49, 54)( 50, 55)( 61, 66)( 62, 67)( 63, 68)( 64, 69)
( 65, 70)( 76, 81)( 77, 82)( 78, 83)( 79, 84)( 80, 85)( 91, 96)( 92, 97)
( 93, 98)( 94, 99)( 95,100)(106,111)(107,112)(108,113)(109,114)(110,115);;
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, 
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2, 
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1 ];;
poly := F / rels;;
 
Permutation Representation (Magma) :
s0 := Sym(120)!(  2,  5)(  3,  4)(  7, 10)(  8,  9)( 12, 15)( 13, 14)( 17, 20)
( 18, 19)( 22, 25)( 23, 24)( 27, 30)( 28, 29)( 31, 46)( 32, 50)( 33, 49)
( 34, 48)( 35, 47)( 36, 51)( 37, 55)( 38, 54)( 39, 53)( 40, 52)( 41, 56)
( 42, 60)( 43, 59)( 44, 58)( 45, 57)( 61, 91)( 62, 95)( 63, 94)( 64, 93)
( 65, 92)( 66, 96)( 67,100)( 68, 99)( 69, 98)( 70, 97)( 71,101)( 72,105)
( 73,104)( 74,103)( 75,102)( 76,106)( 77,110)( 78,109)( 79,108)( 80,107)
( 81,111)( 82,115)( 83,114)( 84,113)( 85,112)( 86,116)( 87,120)( 88,119)
( 89,118)( 90,117);
s1 := Sym(120)!(  1, 62)(  2, 61)(  3, 65)(  4, 64)(  5, 63)(  6, 72)(  7, 71)
(  8, 75)(  9, 74)( 10, 73)( 11, 67)( 12, 66)( 13, 70)( 14, 69)( 15, 68)
( 16, 77)( 17, 76)( 18, 80)( 19, 79)( 20, 78)( 21, 87)( 22, 86)( 23, 90)
( 24, 89)( 25, 88)( 26, 82)( 27, 81)( 28, 85)( 29, 84)( 30, 83)( 31,107)
( 32,106)( 33,110)( 34,109)( 35,108)( 36,117)( 37,116)( 38,120)( 39,119)
( 40,118)( 41,112)( 42,111)( 43,115)( 44,114)( 45,113)( 46, 92)( 47, 91)
( 48, 95)( 49, 94)( 50, 93)( 51,102)( 52,101)( 53,105)( 54,104)( 55,103)
( 56, 97)( 57, 96)( 58,100)( 59, 99)( 60, 98);
s2 := Sym(120)!(  1,  6)(  2,  7)(  3,  8)(  4,  9)(  5, 10)( 16, 21)( 17, 22)
( 18, 23)( 19, 24)( 20, 25)( 31, 36)( 32, 37)( 33, 38)( 34, 39)( 35, 40)
( 46, 51)( 47, 52)( 48, 53)( 49, 54)( 50, 55)( 61, 66)( 62, 67)( 63, 68)
( 64, 69)( 65, 70)( 76, 81)( 77, 82)( 78, 83)( 79, 84)( 80, 85)( 91, 96)
( 92, 97)( 93, 98)( 94, 99)( 95,100)(106,111)(107,112)(108,113)(109,114)
(110,115);
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, 
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2, 
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1 >; 
 
References : None.
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