Polytope of Type {2,2,4,10}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,2,4,10}*1600
if this polytope has a name.
Group : SmallGroup(1600,10271)
Rank : 5
Schlafli Type : {2,2,4,10}
Number of vertices, edges, etc : 2, 2, 20, 100, 50
Order of s₀s₁s₂s₃s₄ : 4
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 : {2,2,4,10}*800
   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 := (3,4);;
s2 := (  6, 15)(  7, 25)(  8, 10)(  9, 20)( 11, 18)( 12, 28)( 14, 23)( 17, 26)
( 19, 21)( 22, 29)( 31, 40)( 32, 50)( 33, 35)( 34, 45)( 36, 43)( 37, 53)
( 39, 48)( 42, 51)( 44, 46)( 47, 54)( 56, 65)( 57, 75)( 58, 60)( 59, 70)
( 61, 68)( 62, 78)( 64, 73)( 67, 76)( 69, 71)( 72, 79)( 81, 90)( 82,100)
( 83, 85)( 84, 95)( 86, 93)( 87,103)( 89, 98)( 92,101)( 94, 96)( 97,104);;
s3 := (  5, 55)(  6, 60)(  7, 65)(  8, 70)(  9, 75)( 10, 56)( 11, 61)( 12, 66)
( 13, 71)( 14, 76)( 15, 57)( 16, 62)( 17, 67)( 18, 72)( 19, 77)( 20, 58)
( 21, 63)( 22, 68)( 23, 73)( 24, 78)( 25, 59)( 26, 64)( 27, 69)( 28, 74)
( 29, 79)( 30, 80)( 31, 85)( 32, 90)( 33, 95)( 34,100)( 35, 81)( 36, 86)
( 37, 91)( 38, 96)( 39,101)( 40, 82)( 41, 87)( 42, 92)( 43, 97)( 44,102)
( 45, 83)( 46, 88)( 47, 93)( 48, 98)( 49,103)( 50, 84)( 51, 89)( 52, 94)
( 53, 99)( 54,104);;
s4 := (  5, 41)(  6, 40)(  7, 44)(  8, 43)(  9, 42)( 10, 36)( 11, 35)( 12, 39)
( 13, 38)( 14, 37)( 15, 31)( 16, 30)( 17, 34)( 18, 33)( 19, 32)( 20, 51)
( 21, 50)( 22, 54)( 23, 53)( 24, 52)( 25, 46)( 26, 45)( 27, 49)( 28, 48)
( 29, 47)( 55, 91)( 56, 90)( 57, 94)( 58, 93)( 59, 92)( 60, 86)( 61, 85)
( 62, 89)( 63, 88)( 64, 87)( 65, 81)( 66, 80)( 67, 84)( 68, 83)( 69, 82)
( 70,101)( 71,100)( 72,104)( 73,103)( 74,102)( 75, 96)( 76, 95)( 77, 99)
( 78, 98)( 79, 97);;
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, s1*s2*s1*s2, s0*s3*s0*s3, 
s1*s3*s1*s3, s0*s4*s0*s4, s1*s4*s1*s4, 
s2*s4*s2*s4, s2*s3*s2*s3*s2*s3*s2*s3, 
s4*s2*s3*s4*s2*s3*s4*s2*s3*s4*s2*s3, 
s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4 ];;
poly := F / rels;;

Permutation Representation (Magma) :

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

to this polytope