Polytope of Type {2,52,4,2}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,52,4,2}*1664
if this polytope has a name.
Group : SmallGroup(1664,17727)
Rank : 5
Schlafli Type : {2,52,4,2}
Number of vertices, edges, etc : 2, 52, 104, 4, 2
Order of s₀s₁s₂s₃s₄ : 52
Order of s₀s₁s₂s₃s₄s₃s₂s₁ : 2
Special Properties :
   Degenerate
   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) :
   2-fold quotients : {2,52,2,2}*832, {2,26,4,2}*832
   4-fold quotients : {2,26,2,2}*416
   8-fold quotients : {2,13,2,2}*208
   13-fold quotients : {2,4,4,2}*128
   26-fold quotients : {2,2,4,2}*64, {2,4,2,2}*64
   52-fold quotients : {2,2,2,2}*32
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)( 17, 28)( 18, 27)
( 19, 26)( 20, 25)( 21, 24)( 22, 23)( 30, 41)( 31, 40)( 32, 39)( 33, 38)
( 34, 37)( 35, 36)( 43, 54)( 44, 53)( 45, 52)( 46, 51)( 47, 50)( 48, 49)
( 55, 81)( 56, 93)( 57, 92)( 58, 91)( 59, 90)( 60, 89)( 61, 88)( 62, 87)
( 63, 86)( 64, 85)( 65, 84)( 66, 83)( 67, 82)( 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, 69)( 17, 68)( 18, 80)
( 19, 79)( 20, 78)( 21, 77)( 22, 76)( 23, 75)( 24, 74)( 25, 73)( 26, 72)
( 27, 71)( 28, 70)( 29, 82)( 30, 81)( 31, 93)( 32, 92)( 33, 91)( 34, 90)
( 35, 89)( 36, 88)( 37, 87)( 38, 86)( 39, 85)( 40, 84)( 41, 83)( 42, 95)
( 43, 94)( 44,106)( 45,105)( 46,104)( 47,103)( 48,102)( 49,101)( 50,100)
( 51, 99)( 52, 98)( 53, 97)( 54, 96);;
s3 := ( 55, 68)( 56, 69)( 57, 70)( 58, 71)( 59, 72)( 60, 73)( 61, 74)( 62, 75)
( 63, 76)( 64, 77)( 65, 78)( 66, 79)( 67, 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);;
s4 := (107,108);;
poly := Group([s0,s1,s2,s3,s4]);;

Finitely Presented Group Representation (GAP) :

F := FreeGroup("s0","s1","s2","s3","s4");;
s0 := F.1;;  s1 := F.2;;  s2 := F.3;;  s3 := F.4;;  s4 := F.5;;  
rels := [ s0*s0, s1*s1, s2*s2, s3*s3, s4*s4, s0*s1*s0*s1, 
s0*s2*s0*s2, s0*s3*s0*s3, s1*s3*s1*s3, 
s0*s4*s0*s4, s1*s4*s1*s4, s2*s4*s2*s4, 
s3*s4*s3*s4, s1*s2*s3*s2*s1*s2*s3*s2, 
s2*s3*s2*s3*s2*s3*s2*s3, 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*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(108)!(1,2);
s1 := Sym(108)!(  4, 15)(  5, 14)(  6, 13)(  7, 12)(  8, 11)(  9, 10)( 17, 28)
( 18, 27)( 19, 26)( 20, 25)( 21, 24)( 22, 23)( 30, 41)( 31, 40)( 32, 39)
( 33, 38)( 34, 37)( 35, 36)( 43, 54)( 44, 53)( 45, 52)( 46, 51)( 47, 50)
( 48, 49)( 55, 81)( 56, 93)( 57, 92)( 58, 91)( 59, 90)( 60, 89)( 61, 88)
( 62, 87)( 63, 86)( 64, 85)( 65, 84)( 66, 83)( 67, 82)( 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(108)!(  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, 69)( 17, 68)
( 18, 80)( 19, 79)( 20, 78)( 21, 77)( 22, 76)( 23, 75)( 24, 74)( 25, 73)
( 26, 72)( 27, 71)( 28, 70)( 29, 82)( 30, 81)( 31, 93)( 32, 92)( 33, 91)
( 34, 90)( 35, 89)( 36, 88)( 37, 87)( 38, 86)( 39, 85)( 40, 84)( 41, 83)
( 42, 95)( 43, 94)( 44,106)( 45,105)( 46,104)( 47,103)( 48,102)( 49,101)
( 50,100)( 51, 99)( 52, 98)( 53, 97)( 54, 96);
s3 := Sym(108)!( 55, 68)( 56, 69)( 57, 70)( 58, 71)( 59, 72)( 60, 73)( 61, 74)
( 62, 75)( 63, 76)( 64, 77)( 65, 78)( 66, 79)( 67, 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);
s4 := Sym(108)!(107,108);
poly := sub<Sym(108)|s0,s1,s2,s3,s4>;

Finitely Presented Group Representation (Magma) :

poly<s0,s1,s2,s3,s4> := Group< s0,s1,s2,s3,s4 | s0*s0, s1*s1, s2*s2, 
s3*s3, s4*s4, s0*s1*s0*s1, s0*s2*s0*s2, 
s0*s3*s0*s3, s1*s3*s1*s3, s0*s4*s0*s4, 
s1*s4*s1*s4, s2*s4*s2*s4, s3*s4*s3*s4, 
s1*s2*s3*s2*s1*s2*s3*s2, s2*s3*s2*s3*s2*s3*s2*s3, 
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*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