Polytope of Type {6,39}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {6,39}*1404
if this polytope has a name.
Group : SmallGroup(1404,122)
Rank : 3
Schlafli Type : {6,39}
Number of vertices, edges, etc : 18, 351, 117
Order of s₀s₁s₂ : 78
Order of s₀s₁s₂s₁ : 6
Special Properties :
   Compact Hyperbolic Quotient
   Locally Spherical
   Orientable
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 : {6,39}*468
   9-fold quotients : {2,39}*156
   13-fold quotients : {6,3}*108
   27-fold quotients : {2,13}*52
   39-fold quotients : {6,3}*36
   117-fold quotients : {2,3}*12
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :

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

Permutation Representation (Magma) :

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

References : None.
to this polytope