Polytope of Type {2,20,4}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,20,4}*2000
if this polytope has a name.
Group : SmallGroup(2000,482)
Rank : 4
Schlafli Type : {2,20,4}
Number of vertices, edges, etc : 2, 125, 250, 25
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 := (  3,  4)(  5,  7)(  8, 97)(  9, 96)( 10, 95)( 11, 94)( 12, 93)( 13, 34)
( 14, 33)( 15, 37)( 16, 36)( 17, 35)( 18,125)( 19,124)( 20,123)( 21,127)
( 22,126)( 23, 65)( 24, 64)( 25, 63)( 26, 67)( 27, 66)( 28, 74)( 29, 73)
( 30, 77)( 31, 76)( 32, 75)( 38, 78)( 39, 82)( 40, 81)( 41, 80)( 42, 79)
( 43, 46)( 44, 45)( 48,108)( 49,112)( 50,111)( 51,110)( 52,109)( 53,122)
( 54,121)( 55,120)( 56,119)( 57,118)( 58, 59)( 60, 62)( 68, 90)( 69, 89)
( 70, 88)( 71, 92)( 72, 91)( 83,107)( 84,106)( 85,105)( 86,104)( 87,103)
( 99,102)(100,101)(114,117)(115,116);;
s3 := (  3, 42)(  4, 41)(  5, 40)(  6, 39)(  7, 38)(  8,  9)( 10, 12)( 13,107)
( 14,106)( 15,105)( 16,104)( 17,103)( 18,101)( 19,100)( 20, 99)( 21, 98)
( 22,102)( 23, 71)( 24, 70)( 25, 69)( 26, 68)( 27, 72)( 28, 67)( 29, 66)
( 30, 65)( 31, 64)( 32, 63)( 33, 34)( 35, 37)( 43,126)( 44,125)( 45,124)
( 46,123)( 47,127)( 48, 96)( 49, 95)( 50, 94)( 51, 93)( 52, 97)( 53, 92)
( 54, 91)( 55, 90)( 56, 89)( 57, 88)( 58, 59)( 60, 62)( 73,121)( 74,120)
( 75,119)( 76,118)( 77,122)( 78,117)( 79,116)( 80,115)( 81,114)( 82,113)
( 83, 84)( 85, 87)(108,109)(110,112);;
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*s1*s2*s1*s2*s1*s2*s3*s1*s2*s1*s2*s1*s2*s1*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)!(  3,  4)(  5,  7)(  8, 97)(  9, 96)( 10, 95)( 11, 94)( 12, 93)
( 13, 34)( 14, 33)( 15, 37)( 16, 36)( 17, 35)( 18,125)( 19,124)( 20,123)
( 21,127)( 22,126)( 23, 65)( 24, 64)( 25, 63)( 26, 67)( 27, 66)( 28, 74)
( 29, 73)( 30, 77)( 31, 76)( 32, 75)( 38, 78)( 39, 82)( 40, 81)( 41, 80)
( 42, 79)( 43, 46)( 44, 45)( 48,108)( 49,112)( 50,111)( 51,110)( 52,109)
( 53,122)( 54,121)( 55,120)( 56,119)( 57,118)( 58, 59)( 60, 62)( 68, 90)
( 69, 89)( 70, 88)( 71, 92)( 72, 91)( 83,107)( 84,106)( 85,105)( 86,104)
( 87,103)( 99,102)(100,101)(114,117)(115,116);
s3 := Sym(127)!(  3, 42)(  4, 41)(  5, 40)(  6, 39)(  7, 38)(  8,  9)( 10, 12)
( 13,107)( 14,106)( 15,105)( 16,104)( 17,103)( 18,101)( 19,100)( 20, 99)
( 21, 98)( 22,102)( 23, 71)( 24, 70)( 25, 69)( 26, 68)( 27, 72)( 28, 67)
( 29, 66)( 30, 65)( 31, 64)( 32, 63)( 33, 34)( 35, 37)( 43,126)( 44,125)
( 45,124)( 46,123)( 47,127)( 48, 96)( 49, 95)( 50, 94)( 51, 93)( 52, 97)
( 53, 92)( 54, 91)( 55, 90)( 56, 89)( 57, 88)( 58, 59)( 60, 62)( 73,121)
( 74,120)( 75,119)( 76,118)( 77,122)( 78,117)( 79,116)( 80,115)( 81,114)
( 82,113)( 83, 84)( 85, 87)(108,109)(110,112);
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, s2*s3*s2*s3*s2*s3*s2*s3, 
s3*s1*s2*s1*s2*s1*s2*s1*s2*s3*s1*s2*s1*s2*s1*s2*s1*s2, 
s1*s2*s3*s2*s1*s2*s3*s2*s1*s2*s3*s2*s1*s2*s3*s2*s1*s2*s3*s2 >;

to this polytope