Polytope of Type {10,20,2}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {10,20,2}*2000e
if this polytope has a name.
Group : SmallGroup(2000,942)
Rank : 4
Schlafli Type : {10,20,2}
Number of vertices, edges, etc : 25, 250, 50, 2
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 : {10,4,2}*400
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :

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

Permutation Representation (Magma) :

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

to this polytope