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

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,10,20,2}*1600a
if this polytope has a name.
Group : SmallGroup(1600,10161)
Rank : 5
Schlafli Type : {2,10,20,2}
Number of vertices, edges, etc : 2, 10, 100, 20, 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}*800a
   5-fold quotients : {2,2,20,2}*320, {2,10,4,2}*320
   10-fold quotients : {2,2,10,2}*160, {2,10,2,2}*160
   20-fold quotients : {2,2,5,2}*80, {2,5,2,2}*80
   25-fold quotients : {2,2,4,2}*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)( 54, 57)( 55, 56)( 59, 62)( 60, 61)
( 64, 67)( 65, 66)( 69, 72)( 70, 71)( 74, 77)( 75, 76)( 79, 82)( 80, 81)
( 84, 87)( 85, 86)( 89, 92)( 90, 91)( 94, 97)( 95, 96)( 99,102)(100,101);;
s2 := (  3,  4)(  5,  7)(  8, 24)(  9, 23)( 10, 27)( 11, 26)( 12, 25)( 13, 19)
( 14, 18)( 15, 22)( 16, 21)( 17, 20)( 28, 29)( 30, 32)( 33, 49)( 34, 48)
( 35, 52)( 36, 51)( 37, 50)( 38, 44)( 39, 43)( 40, 47)( 41, 46)( 42, 45)
( 53, 79)( 54, 78)( 55, 82)( 56, 81)( 57, 80)( 58, 99)( 59, 98)( 60,102)
( 61,101)( 62,100)( 63, 94)( 64, 93)( 65, 97)( 66, 96)( 67, 95)( 68, 89)
( 69, 88)( 70, 92)( 71, 91)( 72, 90)( 73, 84)( 74, 83)( 75, 87)( 76, 86)
( 77, 85);;
s3 := (  3, 58)(  4, 59)(  5, 60)(  6, 61)(  7, 62)(  8, 53)(  9, 54)( 10, 55)
( 11, 56)( 12, 57)( 13, 73)( 14, 74)( 15, 75)( 16, 76)( 17, 77)( 18, 68)
( 19, 69)( 20, 70)( 21, 71)( 22, 72)( 23, 63)( 24, 64)( 25, 65)( 26, 66)
( 27, 67)( 28, 83)( 29, 84)( 30, 85)( 31, 86)( 32, 87)( 33, 78)( 34, 79)
( 35, 80)( 36, 81)( 37, 82)( 38, 98)( 39, 99)( 40,100)( 41,101)( 42,102)
( 43, 93)( 44, 94)( 45, 95)( 46, 96)( 47, 97)( 48, 88)( 49, 89)( 50, 90)
( 51, 91)( 52, 92);;
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, s1*s2*s3*s2*s1*s2*s3*s2, 
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2, 
s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*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)( 54, 57)( 55, 56)( 59, 62)
( 60, 61)( 64, 67)( 65, 66)( 69, 72)( 70, 71)( 74, 77)( 75, 76)( 79, 82)
( 80, 81)( 84, 87)( 85, 86)( 89, 92)( 90, 91)( 94, 97)( 95, 96)( 99,102)
(100,101);
s2 := Sym(104)!(  3,  4)(  5,  7)(  8, 24)(  9, 23)( 10, 27)( 11, 26)( 12, 25)
( 13, 19)( 14, 18)( 15, 22)( 16, 21)( 17, 20)( 28, 29)( 30, 32)( 33, 49)
( 34, 48)( 35, 52)( 36, 51)( 37, 50)( 38, 44)( 39, 43)( 40, 47)( 41, 46)
( 42, 45)( 53, 79)( 54, 78)( 55, 82)( 56, 81)( 57, 80)( 58, 99)( 59, 98)
( 60,102)( 61,101)( 62,100)( 63, 94)( 64, 93)( 65, 97)( 66, 96)( 67, 95)
( 68, 89)( 69, 88)( 70, 92)( 71, 91)( 72, 90)( 73, 84)( 74, 83)( 75, 87)
( 76, 86)( 77, 85);
s3 := Sym(104)!(  3, 58)(  4, 59)(  5, 60)(  6, 61)(  7, 62)(  8, 53)(  9, 54)
( 10, 55)( 11, 56)( 12, 57)( 13, 73)( 14, 74)( 15, 75)( 16, 76)( 17, 77)
( 18, 68)( 19, 69)( 20, 70)( 21, 71)( 22, 72)( 23, 63)( 24, 64)( 25, 65)
( 26, 66)( 27, 67)( 28, 83)( 29, 84)( 30, 85)( 31, 86)( 32, 87)( 33, 78)
( 34, 79)( 35, 80)( 36, 81)( 37, 82)( 38, 98)( 39, 99)( 40,100)( 41,101)
( 42,102)( 43, 93)( 44, 94)( 45, 95)( 46, 96)( 47, 97)( 48, 88)( 49, 89)
( 50, 90)( 51, 91)( 52, 92);
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, 
s1*s2*s3*s2*s1*s2*s3*s2, s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2, 
s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3 >;

to this polytope