Polytope of Type {2,104,2}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,104,2}*832
if this polytope has a name.
Group : SmallGroup(832,1411)
Rank : 4
Schlafli Type : {2,104,2}
Number of vertices, edges, etc : 2, 104, 104, 2
Order of s₀s₁s₂s₃ : 104
Order of s₀s₁s₂s₃s₂s₁ : 2
Special Properties :
   Degenerate
   Universal
   Orientable
   Flat
   Self-Dual
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   {2,104,2,2} of size 1664
Vertex Figure Of :
   {2,2,104,2} of size 1664
Quotients (Maximal Quotients in Boldface) :
   2-fold quotients : {2,52,2}*416
   4-fold quotients : {2,26,2}*208
   8-fold quotients : {2,13,2}*104
   13-fold quotients : {2,8,2}*64
   26-fold quotients : {2,4,2}*32
   52-fold quotients : {2,2,2}*16
Covers (Minimal Covers in Boldface) :
   2-fold covers : {2,104,4}*1664a, {4,104,2}*1664a, {2,208,2}*1664
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)( 29, 42)( 30, 54)( 31, 53)( 32, 52)
( 33, 51)( 34, 50)( 35, 49)( 36, 48)( 37, 47)( 38, 46)( 39, 45)( 40, 44)
( 41, 43)( 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, 95)( 30, 94)( 31,106)( 32,105)( 33,104)( 34,103)
( 35,102)( 36,101)( 37,100)( 38, 99)( 39, 98)( 40, 97)( 41, 96)( 42, 82)
( 43, 81)( 44, 93)( 45, 92)( 46, 91)( 47, 90)( 48, 89)( 49, 88)( 50, 87)
( 51, 86)( 52, 85)( 53, 84)( 54, 83);;
s3 := (107,108);;
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, 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*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)( 29, 42)( 30, 54)( 31, 53)
( 32, 52)( 33, 51)( 34, 50)( 35, 49)( 36, 48)( 37, 47)( 38, 46)( 39, 45)
( 40, 44)( 41, 43)( 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, 95)( 30, 94)( 31,106)( 32,105)( 33,104)
( 34,103)( 35,102)( 36,101)( 37,100)( 38, 99)( 39, 98)( 40, 97)( 41, 96)
( 42, 82)( 43, 81)( 44, 93)( 45, 92)( 46, 91)( 47, 90)( 48, 89)( 49, 88)
( 50, 87)( 51, 86)( 52, 85)( 53, 84)( 54, 83);
s3 := Sym(108)!(107,108);
poly := sub<Sym(108)|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, 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*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