Polytope of Type {2,4,20}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,4,20}*2000
if this polytope has a name.
Group : SmallGroup(2000,482)
Rank : 4
Schlafli Type : {2,4,20}
Number of vertices, edges, etc : 2, 25, 250, 125
Order of s₀s₁s₂s₃ : 10
Order of s₀s₁s₂s₃s₂s₁ : 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) :
   5-fold quotients : {2,4,4}*400
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :

s0 := (1,2);;
s1 := (  4,  7)(  5,  6)(  8, 34)(  9, 33)( 10, 37)( 11, 36)( 12, 35)( 13, 66)
( 14, 65)( 15, 64)( 16, 63)( 17, 67)( 18, 94)( 19, 93)( 20, 97)( 21, 96)
( 22, 95)( 23,123)( 24,127)( 25,126)( 26,125)( 27,124)( 28,103)( 29,107)
( 30,106)( 31,105)( 32,104)( 38, 41)( 39, 40)( 43, 69)( 44, 68)( 45, 72)
( 46, 71)( 47, 70)( 48, 98)( 49,102)( 50,101)( 51,100)( 52, 99)( 53, 78)
( 54, 82)( 55, 81)( 56, 80)( 57, 79)( 58,109)( 59,108)( 60,112)( 61,111)
( 62,110)( 74, 77)( 75, 76)( 83, 84)( 85, 87)( 88,116)( 89,115)( 90,114)
( 91,113)( 92,117)(118,119)(120,122);;
s2 := (  4,  7)(  5,  6)(  8, 96)(  9, 95)( 10, 94)( 11, 93)( 12, 97)( 13, 33)
( 14, 37)( 15, 36)( 16, 35)( 17, 34)( 18,124)( 19,123)( 20,127)( 21,126)
( 22,125)( 23, 64)( 24, 63)( 25, 67)( 26, 66)( 27, 65)( 28, 73)( 29, 77)
( 30, 76)( 31, 75)( 32, 74)( 38, 82)( 39, 81)( 40, 80)( 41, 79)( 42, 78)
( 43, 45)( 46, 47)( 48,112)( 49,111)( 50,110)( 51,109)( 52,108)( 53,121)
( 54,120)( 55,119)( 56,118)( 57,122)( 59, 62)( 60, 61)( 68, 89)( 69, 88)
( 70, 92)( 71, 91)( 72, 90)( 83,106)( 84,105)( 85,104)( 86,103)( 87,107)
( 98,102)( 99,101)(113,117)(114,116);;
s3 := (  3, 73)(  4, 77)(  5, 76)(  6, 75)(  7, 74)(  8, 44)(  9, 43)( 10, 47)
( 11, 46)( 12, 45)( 13, 16)( 14, 15)( 18,109)( 19,108)( 20,112)( 21,111)
( 22,110)( 23, 78)( 24, 82)( 25, 81)( 26, 80)( 27, 79)( 28, 98)( 29,102)
( 30,101)( 31,100)( 32, 99)( 33, 69)( 34, 68)( 35, 72)( 36, 71)( 37, 70)
( 38, 41)( 39, 40)( 48,103)( 49,107)( 50,106)( 51,105)( 52,104)( 53,123)
( 54,127)( 55,126)( 56,125)( 57,124)( 58, 94)( 59, 93)( 60, 97)( 61, 96)
( 62, 95)( 63, 66)( 64, 65)( 83,119)( 84,118)( 85,122)( 86,121)( 87,120)
( 88, 91)( 89, 90)(113,116)(114,115);;
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*s2*s3*s2*s3*s2*s3*s1*s2*s3*s2*s3*s2*s3*s2, 
s1*s2*s3*s2*s1*s2*s3*s2*s1*s2*s3*s2*s1*s2*s3*s2*s1*s2*s3*s2 ];;
poly := F / rels;;

Permutation Representation (Magma) :

s0 := Sym(127)!(1,2);
s1 := Sym(127)!(  4,  7)(  5,  6)(  8, 34)(  9, 33)( 10, 37)( 11, 36)( 12, 35)
( 13, 66)( 14, 65)( 15, 64)( 16, 63)( 17, 67)( 18, 94)( 19, 93)( 20, 97)
( 21, 96)( 22, 95)( 23,123)( 24,127)( 25,126)( 26,125)( 27,124)( 28,103)
( 29,107)( 30,106)( 31,105)( 32,104)( 38, 41)( 39, 40)( 43, 69)( 44, 68)
( 45, 72)( 46, 71)( 47, 70)( 48, 98)( 49,102)( 50,101)( 51,100)( 52, 99)
( 53, 78)( 54, 82)( 55, 81)( 56, 80)( 57, 79)( 58,109)( 59,108)( 60,112)
( 61,111)( 62,110)( 74, 77)( 75, 76)( 83, 84)( 85, 87)( 88,116)( 89,115)
( 90,114)( 91,113)( 92,117)(118,119)(120,122);
s2 := Sym(127)!(  4,  7)(  5,  6)(  8, 96)(  9, 95)( 10, 94)( 11, 93)( 12, 97)
( 13, 33)( 14, 37)( 15, 36)( 16, 35)( 17, 34)( 18,124)( 19,123)( 20,127)
( 21,126)( 22,125)( 23, 64)( 24, 63)( 25, 67)( 26, 66)( 27, 65)( 28, 73)
( 29, 77)( 30, 76)( 31, 75)( 32, 74)( 38, 82)( 39, 81)( 40, 80)( 41, 79)
( 42, 78)( 43, 45)( 46, 47)( 48,112)( 49,111)( 50,110)( 51,109)( 52,108)
( 53,121)( 54,120)( 55,119)( 56,118)( 57,122)( 59, 62)( 60, 61)( 68, 89)
( 69, 88)( 70, 92)( 71, 91)( 72, 90)( 83,106)( 84,105)( 85,104)( 86,103)
( 87,107)( 98,102)( 99,101)(113,117)(114,116);
s3 := Sym(127)!(  3, 73)(  4, 77)(  5, 76)(  6, 75)(  7, 74)(  8, 44)(  9, 43)
( 10, 47)( 11, 46)( 12, 45)( 13, 16)( 14, 15)( 18,109)( 19,108)( 20,112)
( 21,111)( 22,110)( 23, 78)( 24, 82)( 25, 81)( 26, 80)( 27, 79)( 28, 98)
( 29,102)( 30,101)( 31,100)( 32, 99)( 33, 69)( 34, 68)( 35, 72)( 36, 71)
( 37, 70)( 38, 41)( 39, 40)( 48,103)( 49,107)( 50,106)( 51,105)( 52,104)
( 53,123)( 54,127)( 55,126)( 56,125)( 57,124)( 58, 94)( 59, 93)( 60, 97)
( 61, 96)( 62, 95)( 63, 66)( 64, 65)( 83,119)( 84,118)( 85,122)( 86,121)
( 87,120)( 88, 91)( 89, 90)(113,116)(114,115);
poly := sub<Sym(127)|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*s2*s3*s2*s3*s2*s3*s1*s2*s3*s2*s3*s2*s3*s2, 
s1*s2*s3*s2*s1*s2*s3*s2*s1*s2*s3*s2*s1*s2*s3*s2*s1*s2*s3*s2 >;

to this polytope