Polytope of Type {39,6,3}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {39,6,3}*1404
if this polytope has a name.
Group : SmallGroup(1404,122)
Rank : 4
Schlafli Type : {39,6,3}
Number of vertices, edges, etc : 39, 117, 9, 3
Order of s₀s₁s₂s₃ : 39
Order of s₀s₁s₂s₃s₂s₁ : 6
Special Properties :
   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) :
   3-fold quotients : {39,2,3}*468
   9-fold quotients : {13,2,3}*156
   13-fold quotients : {3,6,3}*108
   39-fold quotients : {3,2,3}*36
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :

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

Finitely Presented Group Representation (GAP) :

F := FreeGroup("s0","s1","s2","s3");;
s0 := F.1;;  s1 := F.2;;  s2 := F.3;;  s3 := F.4;;  
rels := [ s0*s0, s1*s1, s2*s2, s3*s3, s0*s2*s0*s2, 
s0*s3*s0*s3, s1*s3*s1*s3, s2*s3*s2*s3*s2*s3, 
s2*s0*s1*s2*s1*s2*s0*s1*s2*s1, s3*s1*s2*s1*s2*s3*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 ];;
poly := F / rels;;

Permutation Representation (Magma) :

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

Finitely Presented Group Representation (Magma) :

poly<s0,s1,s2,s3> := Group< s0,s1,s2,s3 | s0*s0, s1*s1, s2*s2, 
s3*s3, s0*s2*s0*s2, s0*s3*s0*s3, s1*s3*s1*s3, 
s2*s3*s2*s3*s2*s3, s2*s0*s1*s2*s1*s2*s0*s1*s2*s1, 
s3*s1*s2*s1*s2*s3*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 >;

References : None.
to this polytope