Polytope of Type {2,39,6}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,39,6}*936
if this polytope has a name.
Group : SmallGroup(936,212)
Rank : 4
Schlafli Type : {2,39,6}
Number of vertices, edges, etc : 2, 39, 117, 6
Order of s₀s₁s₂s₃ : 78
Order of s₀s₁s₂s₃s₂s₁ : 2
Special Properties :
   Degenerate
   Universal
   Orientable
   Flat
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   {2,39,6,2} of size 1872
Vertex Figure Of :
   {2,2,39,6} of size 1872
Quotients (Maximal Quotients in Boldface) :
   3-fold quotients : {2,39,2}*312
   9-fold quotients : {2,13,2}*104
   13-fold quotients : {2,3,6}*72
   39-fold quotients : {2,3,2}*24
Covers (Minimal Covers in Boldface) :
   2-fold covers : {2,78,6}*1872c
Permutation Representation (GAP) :

s0 := (1,2);;
s1 := (  4, 15)(  5, 14)(  6, 13)(  7, 12)(  8, 11)(  9, 10)( 16, 29)( 17, 41)
( 18, 40)( 19, 39)( 20, 38)( 21, 37)( 22, 36)( 23, 35)( 24, 34)( 25, 33)
( 26, 32)( 27, 31)( 28, 30)( 42, 81)( 43, 93)( 44, 92)( 45, 91)( 46, 90)
( 47, 89)( 48, 88)( 49, 87)( 50, 86)( 51, 85)( 52, 84)( 53, 83)( 54, 82)
( 55,107)( 56,119)( 57,118)( 58,117)( 59,116)( 60,115)( 61,114)( 62,113)
( 63,112)( 64,111)( 65,110)( 66,109)( 67,108)( 68, 94)( 69,106)( 70,105)
( 71,104)( 72,103)( 73,102)( 74,101)( 75,100)( 76, 99)( 77, 98)( 78, 97)
( 79, 96)( 80, 95);;
s2 := (  3, 56)(  4, 55)(  5, 67)(  6, 66)(  7, 65)(  8, 64)(  9, 63)( 10, 62)
( 11, 61)( 12, 60)( 13, 59)( 14, 58)( 15, 57)( 16, 43)( 17, 42)( 18, 54)
( 19, 53)( 20, 52)( 21, 51)( 22, 50)( 23, 49)( 24, 48)( 25, 47)( 26, 46)
( 27, 45)( 28, 44)( 29, 69)( 30, 68)( 31, 80)( 32, 79)( 33, 78)( 34, 77)
( 35, 76)( 36, 75)( 37, 74)( 38, 73)( 39, 72)( 40, 71)( 41, 70)( 81, 95)
( 82, 94)( 83,106)( 84,105)( 85,104)( 86,103)( 87,102)( 88,101)( 89,100)
( 90, 99)( 91, 98)( 92, 97)( 93, 96)(107,108)(109,119)(110,118)(111,117)
(112,116)(113,115);;
s3 := ( 42, 81)( 43, 82)( 44, 83)( 45, 84)( 46, 85)( 47, 86)( 48, 87)( 49, 88)
( 50, 89)( 51, 90)( 52, 91)( 53, 92)( 54, 93)( 55, 94)( 56, 95)( 57, 96)
( 58, 97)( 59, 98)( 60, 99)( 61,100)( 62,101)( 63,102)( 64,103)( 65,104)
( 66,105)( 67,106)( 68,107)( 69,108)( 70,109)( 71,110)( 72,111)( 73,112)
( 74,113)( 75,114)( 76,115)( 77,116)( 78,117)( 79,118)( 80,119);;
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*s1*s0*s1, 
s0*s2*s0*s2, s0*s3*s0*s3, s1*s3*s1*s3, 
s3*s1*s2*s3*s2*s3*s1*s2*s3*s2, s1*s2*s3*s2*s1*s2*s1*s2*s3*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*s1*s2 ];;
poly := F / rels;;

Permutation Representation (Magma) :

s0 := Sym(119)!(1,2);
s1 := Sym(119)!(  4, 15)(  5, 14)(  6, 13)(  7, 12)(  8, 11)(  9, 10)( 16, 29)
( 17, 41)( 18, 40)( 19, 39)( 20, 38)( 21, 37)( 22, 36)( 23, 35)( 24, 34)
( 25, 33)( 26, 32)( 27, 31)( 28, 30)( 42, 81)( 43, 93)( 44, 92)( 45, 91)
( 46, 90)( 47, 89)( 48, 88)( 49, 87)( 50, 86)( 51, 85)( 52, 84)( 53, 83)
( 54, 82)( 55,107)( 56,119)( 57,118)( 58,117)( 59,116)( 60,115)( 61,114)
( 62,113)( 63,112)( 64,111)( 65,110)( 66,109)( 67,108)( 68, 94)( 69,106)
( 70,105)( 71,104)( 72,103)( 73,102)( 74,101)( 75,100)( 76, 99)( 77, 98)
( 78, 97)( 79, 96)( 80, 95);
s2 := Sym(119)!(  3, 56)(  4, 55)(  5, 67)(  6, 66)(  7, 65)(  8, 64)(  9, 63)
( 10, 62)( 11, 61)( 12, 60)( 13, 59)( 14, 58)( 15, 57)( 16, 43)( 17, 42)
( 18, 54)( 19, 53)( 20, 52)( 21, 51)( 22, 50)( 23, 49)( 24, 48)( 25, 47)
( 26, 46)( 27, 45)( 28, 44)( 29, 69)( 30, 68)( 31, 80)( 32, 79)( 33, 78)
( 34, 77)( 35, 76)( 36, 75)( 37, 74)( 38, 73)( 39, 72)( 40, 71)( 41, 70)
( 81, 95)( 82, 94)( 83,106)( 84,105)( 85,104)( 86,103)( 87,102)( 88,101)
( 89,100)( 90, 99)( 91, 98)( 92, 97)( 93, 96)(107,108)(109,119)(110,118)
(111,117)(112,116)(113,115);
s3 := Sym(119)!( 42, 81)( 43, 82)( 44, 83)( 45, 84)( 46, 85)( 47, 86)( 48, 87)
( 49, 88)( 50, 89)( 51, 90)( 52, 91)( 53, 92)( 54, 93)( 55, 94)( 56, 95)
( 57, 96)( 58, 97)( 59, 98)( 60, 99)( 61,100)( 62,101)( 63,102)( 64,103)
( 65,104)( 66,105)( 67,106)( 68,107)( 69,108)( 70,109)( 71,110)( 72,111)
( 73,112)( 74,113)( 75,114)( 76,115)( 77,116)( 78,117)( 79,118)( 80,119);
poly := sub<Sym(119)|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*s1*s0*s1, s0*s2*s0*s2, s0*s3*s0*s3, 
s1*s3*s1*s3, s3*s1*s2*s3*s2*s3*s1*s2*s3*s2, 
s1*s2*s3*s2*s1*s2*s1*s2*s3*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*s1*s2 >;

to this polytope