Polytope of Type {2,10,4}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,10,4}*2000
if this polytope has a name.
Group : SmallGroup(2000,482)
Rank : 4
Schlafli Type : {2,10,4}
Number of vertices, edges, etc : 2, 125, 250, 50
Order of s₀s₁s₂s₃ : 20
Order of s₀s₁s₂s₃s₂s₁ : 2
Special Properties :
   Degenerate
   Universal
   Non-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 : {2,10,4}*400
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :

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

Permutation Representation (Magma) :

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

to this polytope