Polytope of Type {2,50,4}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,50,4}*800
if this polytope has a name.
Group : SmallGroup(800,220)
Rank : 4
Schlafli Type : {2,50,4}
Number of vertices, edges, etc : 2, 50, 100, 4
Order of s₀s₁s₂s₃ : 100
Order of s₀s₁s₂s₃s₂s₁ : 2
Special Properties :
   Degenerate
   Universal
   Orientable
   Flat
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   {2,50,4,2} of size 1600
Vertex Figure Of :
   {2,2,50,4} of size 1600
Quotients (Maximal Quotients in Boldface) :
   2-fold quotients : {2,50,2}*400
   4-fold quotients : {2,25,2}*200
   5-fold quotients : {2,10,4}*160
   10-fold quotients : {2,10,2}*80
   20-fold quotients : {2,5,2}*40
   25-fold quotients : {2,2,4}*32
   50-fold quotients : {2,2,2}*16
Covers (Minimal Covers in Boldface) :
   2-fold covers : {2,100,4}*1600, {4,50,4}*1600, {2,50,8}*1600
Permutation Representation (GAP) :

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