Polytope of Type {2,20,4}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,20,4}*1600
if this polytope has a name.
Group : SmallGroup(1600,10050)
Rank : 4
Schlafli Type : {2,20,4}
Number of vertices, edges, etc : 2, 100, 200, 20
Order of s₀s₁s₂s₃ : 4
Order of s₀s₁s₂s₃s₂s₁ : 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 : {2,10,4}*800
   4-fold quotients : {2,10,4}*400
   25-fold quotients : {2,4,4}*64
   50-fold quotients : {2,2,4}*32, {2,4,2}*32
   100-fold quotients : {2,2,2}*16
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :

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

to this polytope