Polytope of Type {2,4,10}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,4,10}*800
if this polytope has a name.
Group : SmallGroup(800,1201)
Rank : 4
Schlafli Type : {2,4,10}
Number of vertices, edges, etc : 2, 20, 100, 50
Order of s₀s₁s₂s₃ : 4
Order of s₀s₁s₂s₃s₂s₁ : 2
Special Properties :
   Degenerate
   Universal
   Orientable
   Flat
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   {2,4,10,2} of size 1600
Vertex Figure Of :
   {2,2,4,10} of size 1600
Quotients (Maximal Quotients in Boldface) :
   2-fold quotients : {2,4,10}*400
   25-fold quotients : {2,4,2}*32
   50-fold quotients : {2,2,2}*16
Covers (Minimal Covers in Boldface) :
   2-fold covers : {2,8,10}*1600, {4,4,10}*1600, {2,4,20}*1600
Permutation Representation (GAP) :

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

to this polytope