Polytope of Type {2,4,20}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,4,20}*1600
if this polytope has a name.
Group : SmallGroup(1600,10050)
Rank : 4
Schlafli Type : {2,4,20}
Number of vertices, edges, etc : 2, 20, 200, 100
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 : {2,4,10}*800
   4-fold quotients : {2,4,10}*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 := (  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);;
s2 := (  4, 21)(  5,  9)(  6, 27)(  7, 15)(  8, 17)( 10, 18)( 12, 24)( 13, 26)
( 16, 20)( 19, 23)( 29, 46)( 30, 34)( 31, 52)( 32, 40)( 33, 42)( 35, 43)
( 37, 49)( 38, 51)( 41, 45)( 44, 48)( 53, 78)( 54, 96)( 55, 84)( 56,102)
( 57, 90)( 58, 92)( 59, 80)( 60, 93)( 61, 86)( 62, 99)( 63,101)( 64, 89)
( 65, 82)( 66, 95)( 67, 83)( 68, 85)( 69, 98)( 70, 91)( 71, 79)( 72, 97)
( 73, 94)( 74, 87)( 75,100)( 76, 88)( 77, 81);;
s3 := (  3, 60)(  4, 59)(  5, 58)(  6, 62)(  7, 61)(  8, 55)(  9, 54)( 10, 53)
( 11, 57)( 12, 56)( 13, 75)( 14, 74)( 15, 73)( 16, 77)( 17, 76)( 18, 70)
( 19, 69)( 20, 68)( 21, 72)( 22, 71)( 23, 65)( 24, 64)( 25, 63)( 26, 67)
( 27, 66)( 28, 85)( 29, 84)( 30, 83)( 31, 87)( 32, 86)( 33, 80)( 34, 79)
( 35, 78)( 36, 82)( 37, 81)( 38,100)( 39, 99)( 40, 98)( 41,102)( 42,101)
( 43, 95)( 44, 94)( 45, 93)( 46, 97)( 47, 96)( 48, 90)( 49, 89)( 50, 88)
( 51, 92)( 52, 91);;
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, 
s1*s2*s1*s2*s1*s2*s1*s2, s3*s1*s2*s3*s1*s2*s3*s1*s2*s3*s1*s2, 
s1*s2*s3*s2*s1*s2*s3*s2*s1*s2*s3*s2*s1*s2*s3*s2*s1*s2*s3*s2*s1*s2*s3*s2*s1*s2*s3*s2*s1*s2*s3*s2*s1*s2*s3*s2*s1*s2*s3*s2 ];;
poly := F / rels;;

Permutation Representation (Magma) :

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

to this polytope