Polytope of Type {2,52,6}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,52,6}*1872
if this polytope has a name.
Group : SmallGroup(1872,1058)
Rank : 4
Schlafli Type : {2,52,6}
Number of vertices, edges, etc : 2, 78, 234, 9
Order of s₀s₁s₂s₃ : 52
Order of s₀s₁s₂s₃s₂s₁ : 2
Special Properties :
   Degenerate
   Universal
   Non-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) :
   13-fold quotients : {2,4,6}*144
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :

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

to this polytope