Polytope of Type {2,10,25,2}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,10,25,2}*2000
if this polytope has a name.
Group : SmallGroup(2000,500)
Rank : 5
Schlafli Type : {2,10,25,2}
Number of vertices, edges, etc : 2, 10, 125, 25, 2
Order of s₀s₁s₂s₃s₄ : 50
Order of s₀s₁s₂s₃s₄s₃s₂s₁ : 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 : {2,2,25,2}*400, {2,10,5,2}*400
   25-fold quotients : {2,2,5,2}*80
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :

s0 := (1,2);;
s1 := (  8, 23)(  9, 24)( 10, 25)( 11, 26)( 12, 27)( 13, 18)( 14, 19)( 15, 20)
( 16, 21)( 17, 22)( 33, 48)( 34, 49)( 35, 50)( 36, 51)( 37, 52)( 38, 43)
( 39, 44)( 40, 45)( 41, 46)( 42, 47)( 58, 73)( 59, 74)( 60, 75)( 61, 76)
( 62, 77)( 63, 68)( 64, 69)( 65, 70)( 66, 71)( 67, 72)( 83, 98)( 84, 99)
( 85,100)( 86,101)( 87,102)( 88, 93)( 89, 94)( 90, 95)( 91, 96)( 92, 97)
(108,123)(109,124)(110,125)(111,126)(112,127)(113,118)(114,119)(115,120)
(116,121)(117,122);;
s2 := (  3,  8)(  4, 12)(  5, 11)(  6, 10)(  7,  9)( 13, 23)( 14, 27)( 15, 26)
( 16, 25)( 17, 24)( 19, 22)( 20, 21)( 28,109)( 29,108)( 30,112)( 31,111)
( 32,110)( 33,104)( 34,103)( 35,107)( 36,106)( 37,105)( 38,124)( 39,123)
( 40,127)( 41,126)( 42,125)( 43,119)( 44,118)( 45,122)( 46,121)( 47,120)
( 48,114)( 49,113)( 50,117)( 51,116)( 52,115)( 53, 84)( 54, 83)( 55, 87)
( 56, 86)( 57, 85)( 58, 79)( 59, 78)( 60, 82)( 61, 81)( 62, 80)( 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, 28)(  4, 32)(  5, 31)(  6, 30)(  7, 29)(  8, 48)(  9, 52)( 10, 51)
( 11, 50)( 12, 49)( 13, 43)( 14, 47)( 15, 46)( 16, 45)( 17, 44)( 18, 38)
( 19, 42)( 20, 41)( 21, 40)( 22, 39)( 23, 33)( 24, 37)( 25, 36)( 26, 35)
( 27, 34)( 53,104)( 54,103)( 55,107)( 56,106)( 57,105)( 58,124)( 59,123)
( 60,127)( 61,126)( 62,125)( 63,119)( 64,118)( 65,122)( 66,121)( 67,120)
( 68,114)( 69,113)( 70,117)( 71,116)( 72,115)( 73,109)( 74,108)( 75,112)
( 76,111)( 77,110)( 78, 79)( 80, 82)( 83, 99)( 84, 98)( 85,102)( 86,101)
( 87,100)( 88, 94)( 89, 93)( 90, 97)( 91, 96)( 92, 95);;
s4 := (128,129);;
poly := Group([s0,s1,s2,s3,s4]);;

Finitely Presented Group Representation (GAP) :

F := FreeGroup("s0","s1","s2","s3","s4");;
s0 := F.1;;  s1 := F.2;;  s2 := F.3;;  s3 := F.4;;  s4 := F.5;;  
rels := [ s0*s0, s1*s1, s2*s2, s3*s3, s4*s4, s0*s1*s0*s1, 
s0*s2*s0*s2, s0*s3*s0*s3, s1*s3*s1*s3, 
s0*s4*s0*s4, s1*s4*s1*s4, s2*s4*s2*s4, 
s3*s4*s3*s4, s3*s1*s2*s1*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, 
s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3 ];;
poly := F / rels;;

Permutation Representation (Magma) :

s0 := Sym(129)!(1,2);
s1 := Sym(129)!(  8, 23)(  9, 24)( 10, 25)( 11, 26)( 12, 27)( 13, 18)( 14, 19)
( 15, 20)( 16, 21)( 17, 22)( 33, 48)( 34, 49)( 35, 50)( 36, 51)( 37, 52)
( 38, 43)( 39, 44)( 40, 45)( 41, 46)( 42, 47)( 58, 73)( 59, 74)( 60, 75)
( 61, 76)( 62, 77)( 63, 68)( 64, 69)( 65, 70)( 66, 71)( 67, 72)( 83, 98)
( 84, 99)( 85,100)( 86,101)( 87,102)( 88, 93)( 89, 94)( 90, 95)( 91, 96)
( 92, 97)(108,123)(109,124)(110,125)(111,126)(112,127)(113,118)(114,119)
(115,120)(116,121)(117,122);
s2 := Sym(129)!(  3,  8)(  4, 12)(  5, 11)(  6, 10)(  7,  9)( 13, 23)( 14, 27)
( 15, 26)( 16, 25)( 17, 24)( 19, 22)( 20, 21)( 28,109)( 29,108)( 30,112)
( 31,111)( 32,110)( 33,104)( 34,103)( 35,107)( 36,106)( 37,105)( 38,124)
( 39,123)( 40,127)( 41,126)( 42,125)( 43,119)( 44,118)( 45,122)( 46,121)
( 47,120)( 48,114)( 49,113)( 50,117)( 51,116)( 52,115)( 53, 84)( 54, 83)
( 55, 87)( 56, 86)( 57, 85)( 58, 79)( 59, 78)( 60, 82)( 61, 81)( 62, 80)
( 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(129)!(  3, 28)(  4, 32)(  5, 31)(  6, 30)(  7, 29)(  8, 48)(  9, 52)
( 10, 51)( 11, 50)( 12, 49)( 13, 43)( 14, 47)( 15, 46)( 16, 45)( 17, 44)
( 18, 38)( 19, 42)( 20, 41)( 21, 40)( 22, 39)( 23, 33)( 24, 37)( 25, 36)
( 26, 35)( 27, 34)( 53,104)( 54,103)( 55,107)( 56,106)( 57,105)( 58,124)
( 59,123)( 60,127)( 61,126)( 62,125)( 63,119)( 64,118)( 65,122)( 66,121)
( 67,120)( 68,114)( 69,113)( 70,117)( 71,116)( 72,115)( 73,109)( 74,108)
( 75,112)( 76,111)( 77,110)( 78, 79)( 80, 82)( 83, 99)( 84, 98)( 85,102)
( 86,101)( 87,100)( 88, 94)( 89, 93)( 90, 97)( 91, 96)( 92, 95);
s4 := Sym(129)!(128,129);
poly := sub<Sym(129)|s0,s1,s2,s3,s4>;

Finitely Presented Group Representation (Magma) :

poly<s0,s1,s2,s3,s4> := Group< s0,s1,s2,s3,s4 | s0*s0, s1*s1, s2*s2, 
s3*s3, s4*s4, s0*s1*s0*s1, s0*s2*s0*s2, 
s0*s3*s0*s3, s1*s3*s1*s3, s0*s4*s0*s4, 
s1*s4*s1*s4, s2*s4*s2*s4, s3*s4*s3*s4, 
s3*s1*s2*s1*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, 
s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3 >;

to this polytope