Polytope of Type {2,10,4}

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

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

Permutation Representation (Magma) :

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

to this polytope