Polytope of Type {2,20,10,2}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,20,10,2}*1600c
if this polytope has a name.
Group : SmallGroup(1600,10205)
Rank : 5
Schlafli Type : {2,20,10,2}
Number of vertices, edges, etc : 2, 20, 100, 10, 2
Order of s₀s₁s₂s₃s₄ : 20
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 : {2,10,10,2}*800b
   4-fold quotients : {2,10,5,2}*400
   5-fold quotients : {2,4,10,2}*320
   10-fold quotients : {2,2,10,2}*160
   20-fold quotients : {2,2,5,2}*80
   25-fold quotients : {2,4,2,2}*64
   50-fold quotients : {2,2,2,2}*32
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :

s0 := (1,2);;
s1 := (  4,  7)(  5,  6)(  9, 12)( 10, 11)( 14, 17)( 15, 16)( 19, 22)( 20, 21)
( 24, 27)( 25, 26)( 29, 32)( 30, 31)( 34, 37)( 35, 36)( 39, 42)( 40, 41)
( 44, 47)( 45, 46)( 49, 52)( 50, 51)( 53, 78)( 54, 82)( 55, 81)( 56, 80)
( 57, 79)( 58, 83)( 59, 87)( 60, 86)( 61, 85)( 62, 84)( 63, 88)( 64, 92)
( 65, 91)( 66, 90)( 67, 89)( 68, 93)( 69, 97)( 70, 96)( 71, 95)( 72, 94)
( 73, 98)( 74,102)( 75,101)( 76,100)( 77, 99);;
s2 := (  3, 54)(  4, 53)(  5, 57)(  6, 56)(  7, 55)(  8, 74)(  9, 73)( 10, 77)
( 11, 76)( 12, 75)( 13, 69)( 14, 68)( 15, 72)( 16, 71)( 17, 70)( 18, 64)
( 19, 63)( 20, 67)( 21, 66)( 22, 65)( 23, 59)( 24, 58)( 25, 62)( 26, 61)
( 27, 60)( 28, 79)( 29, 78)( 30, 82)( 31, 81)( 32, 80)( 33, 99)( 34, 98)
( 35,102)( 36,101)( 37,100)( 38, 94)( 39, 93)( 40, 97)( 41, 96)( 42, 95)
( 43, 89)( 44, 88)( 45, 92)( 46, 91)( 47, 90)( 48, 84)( 49, 83)( 50, 87)
( 51, 86)( 52, 85);;
s3 := (  3,  8)(  4, 12)(  5, 11)(  6, 10)(  7,  9)( 13, 23)( 14, 27)( 15, 26)
( 16, 25)( 17, 24)( 19, 22)( 20, 21)( 28, 33)( 29, 37)( 30, 36)( 31, 35)
( 32, 34)( 38, 48)( 39, 52)( 40, 51)( 41, 50)( 42, 49)( 44, 47)( 45, 46)
( 53, 58)( 54, 62)( 55, 61)( 56, 60)( 57, 59)( 63, 73)( 64, 77)( 65, 76)
( 66, 75)( 67, 74)( 69, 72)( 70, 71)( 78, 83)( 79, 87)( 80, 86)( 81, 85)
( 82, 84)( 88, 98)( 89,102)( 90,101)( 91,100)( 92, 99)( 94, 97)( 95, 96);;
s4 := (103,104);;
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, s3*s1*s2*s1*s2*s3*s1*s2*s1*s2, 
s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3 ];;
poly := F / rels;;

Permutation Representation (Magma) :

s0 := Sym(104)!(1,2);
s1 := Sym(104)!(  4,  7)(  5,  6)(  9, 12)( 10, 11)( 14, 17)( 15, 16)( 19, 22)
( 20, 21)( 24, 27)( 25, 26)( 29, 32)( 30, 31)( 34, 37)( 35, 36)( 39, 42)
( 40, 41)( 44, 47)( 45, 46)( 49, 52)( 50, 51)( 53, 78)( 54, 82)( 55, 81)
( 56, 80)( 57, 79)( 58, 83)( 59, 87)( 60, 86)( 61, 85)( 62, 84)( 63, 88)
( 64, 92)( 65, 91)( 66, 90)( 67, 89)( 68, 93)( 69, 97)( 70, 96)( 71, 95)
( 72, 94)( 73, 98)( 74,102)( 75,101)( 76,100)( 77, 99);
s2 := Sym(104)!(  3, 54)(  4, 53)(  5, 57)(  6, 56)(  7, 55)(  8, 74)(  9, 73)
( 10, 77)( 11, 76)( 12, 75)( 13, 69)( 14, 68)( 15, 72)( 16, 71)( 17, 70)
( 18, 64)( 19, 63)( 20, 67)( 21, 66)( 22, 65)( 23, 59)( 24, 58)( 25, 62)
( 26, 61)( 27, 60)( 28, 79)( 29, 78)( 30, 82)( 31, 81)( 32, 80)( 33, 99)
( 34, 98)( 35,102)( 36,101)( 37,100)( 38, 94)( 39, 93)( 40, 97)( 41, 96)
( 42, 95)( 43, 89)( 44, 88)( 45, 92)( 46, 91)( 47, 90)( 48, 84)( 49, 83)
( 50, 87)( 51, 86)( 52, 85);
s3 := Sym(104)!(  3,  8)(  4, 12)(  5, 11)(  6, 10)(  7,  9)( 13, 23)( 14, 27)
( 15, 26)( 16, 25)( 17, 24)( 19, 22)( 20, 21)( 28, 33)( 29, 37)( 30, 36)
( 31, 35)( 32, 34)( 38, 48)( 39, 52)( 40, 51)( 41, 50)( 42, 49)( 44, 47)
( 45, 46)( 53, 58)( 54, 62)( 55, 61)( 56, 60)( 57, 59)( 63, 73)( 64, 77)
( 65, 76)( 66, 75)( 67, 74)( 69, 72)( 70, 71)( 78, 83)( 79, 87)( 80, 86)
( 81, 85)( 82, 84)( 88, 98)( 89,102)( 90,101)( 91,100)( 92, 99)( 94, 97)
( 95, 96);
s4 := Sym(104)!(103,104);
poly := sub<Sym(104)|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, 
s3*s1*s2*s1*s2*s3*s1*s2*s1*s2, s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3 >;

to this polytope