Polytope of Type {2,25,10}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,25,10}*1000
if this polytope has a name.
Group : SmallGroup(1000,105)
Rank : 4
Schlafli Type : {2,25,10}
Number of vertices, edges, etc : 2, 25, 125, 10
Order of s₀s₁s₂s₃ : 50
Order of s₀s₁s₂s₃s₂s₁ : 2
Special Properties :
   Degenerate
   Universal
   Orientable
   Flat
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   {2,25,10,2} of size 2000
Vertex Figure Of :
   {2,2,25,10} of size 2000
Quotients (Maximal Quotients in Boldface) :
   5-fold quotients : {2,25,2}*200, {2,5,10}*200
   25-fold quotients : {2,5,2}*40
Covers (Minimal Covers in Boldface) :
   2-fold covers : {2,50,10}*2000b
Permutation Representation (GAP) :

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

Permutation Representation (Magma) :

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

to this polytope