Polytope of Type {6,52,2}

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

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