Polytope of Type {2,26,10}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,26,10}*1040
if this polytope has a name.
Group : SmallGroup(1040,227)
Rank : 4
Schlafli Type : {2,26,10}
Number of vertices, edges, etc : 2, 26, 130, 10
Order of s₀s₁s₂s₃ : 130
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 : {2,26,2}*208
   10-fold quotients : {2,13,2}*104
   13-fold quotients : {2,2,10}*80
   26-fold quotients : {2,2,5}*40
   65-fold quotients : {2,2,2}*16
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :

s0 := (1,2);;
s1 := (  4, 15)(  5, 14)(  6, 13)(  7, 12)(  8, 11)(  9, 10)( 17, 28)( 18, 27)
( 19, 26)( 20, 25)( 21, 24)( 22, 23)( 30, 41)( 31, 40)( 32, 39)( 33, 38)
( 34, 37)( 35, 36)( 43, 54)( 44, 53)( 45, 52)( 46, 51)( 47, 50)( 48, 49)
( 56, 67)( 57, 66)( 58, 65)( 59, 64)( 60, 63)( 61, 62)( 69, 80)( 70, 79)
( 71, 78)( 72, 77)( 73, 76)( 74, 75)( 82, 93)( 83, 92)( 84, 91)( 85, 90)
( 86, 89)( 87, 88)( 95,106)( 96,105)( 97,104)( 98,103)( 99,102)(100,101)
(108,119)(109,118)(110,117)(111,116)(112,115)(113,114)(121,132)(122,131)
(123,130)(124,129)(125,128)(126,127);;
s2 := (  3,  4)(  5, 15)(  6, 14)(  7, 13)(  8, 12)(  9, 11)( 16, 56)( 17, 55)
( 18, 67)( 19, 66)( 20, 65)( 21, 64)( 22, 63)( 23, 62)( 24, 61)( 25, 60)
( 26, 59)( 27, 58)( 28, 57)( 29, 43)( 30, 42)( 31, 54)( 32, 53)( 33, 52)
( 34, 51)( 35, 50)( 36, 49)( 37, 48)( 38, 47)( 39, 46)( 40, 45)( 41, 44)
( 68, 69)( 70, 80)( 71, 79)( 72, 78)( 73, 77)( 74, 76)( 81,121)( 82,120)
( 83,132)( 84,131)( 85,130)( 86,129)( 87,128)( 88,127)( 89,126)( 90,125)
( 91,124)( 92,123)( 93,122)( 94,108)( 95,107)( 96,119)( 97,118)( 98,117)
( 99,116)(100,115)(101,114)(102,113)(103,112)(104,111)(105,110)(106,109);;
s3 := (  3, 81)(  4, 82)(  5, 83)(  6, 84)(  7, 85)(  8, 86)(  9, 87)( 10, 88)
( 11, 89)( 12, 90)( 13, 91)( 14, 92)( 15, 93)( 16, 68)( 17, 69)( 18, 70)
( 19, 71)( 20, 72)( 21, 73)( 22, 74)( 23, 75)( 24, 76)( 25, 77)( 26, 78)
( 27, 79)( 28, 80)( 29,120)( 30,121)( 31,122)( 32,123)( 33,124)( 34,125)
( 35,126)( 36,127)( 37,128)( 38,129)( 39,130)( 40,131)( 41,132)( 42,107)
( 43,108)( 44,109)( 45,110)( 46,111)( 47,112)( 48,113)( 49,114)( 50,115)
( 51,116)( 52,117)( 53,118)( 54,119)( 55, 94)( 56, 95)( 57, 96)( 58, 97)
( 59, 98)( 60, 99)( 61,100)( 62,101)( 63,102)( 64,103)( 65,104)( 66,105)
( 67,106);;
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, 
s1*s2*s3*s2*s1*s2*s3*s2, s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*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*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(132)!(1,2);
s1 := Sym(132)!(  4, 15)(  5, 14)(  6, 13)(  7, 12)(  8, 11)(  9, 10)( 17, 28)
( 18, 27)( 19, 26)( 20, 25)( 21, 24)( 22, 23)( 30, 41)( 31, 40)( 32, 39)
( 33, 38)( 34, 37)( 35, 36)( 43, 54)( 44, 53)( 45, 52)( 46, 51)( 47, 50)
( 48, 49)( 56, 67)( 57, 66)( 58, 65)( 59, 64)( 60, 63)( 61, 62)( 69, 80)
( 70, 79)( 71, 78)( 72, 77)( 73, 76)( 74, 75)( 82, 93)( 83, 92)( 84, 91)
( 85, 90)( 86, 89)( 87, 88)( 95,106)( 96,105)( 97,104)( 98,103)( 99,102)
(100,101)(108,119)(109,118)(110,117)(111,116)(112,115)(113,114)(121,132)
(122,131)(123,130)(124,129)(125,128)(126,127);
s2 := Sym(132)!(  3,  4)(  5, 15)(  6, 14)(  7, 13)(  8, 12)(  9, 11)( 16, 56)
( 17, 55)( 18, 67)( 19, 66)( 20, 65)( 21, 64)( 22, 63)( 23, 62)( 24, 61)
( 25, 60)( 26, 59)( 27, 58)( 28, 57)( 29, 43)( 30, 42)( 31, 54)( 32, 53)
( 33, 52)( 34, 51)( 35, 50)( 36, 49)( 37, 48)( 38, 47)( 39, 46)( 40, 45)
( 41, 44)( 68, 69)( 70, 80)( 71, 79)( 72, 78)( 73, 77)( 74, 76)( 81,121)
( 82,120)( 83,132)( 84,131)( 85,130)( 86,129)( 87,128)( 88,127)( 89,126)
( 90,125)( 91,124)( 92,123)( 93,122)( 94,108)( 95,107)( 96,119)( 97,118)
( 98,117)( 99,116)(100,115)(101,114)(102,113)(103,112)(104,111)(105,110)
(106,109);
s3 := Sym(132)!(  3, 81)(  4, 82)(  5, 83)(  6, 84)(  7, 85)(  8, 86)(  9, 87)
( 10, 88)( 11, 89)( 12, 90)( 13, 91)( 14, 92)( 15, 93)( 16, 68)( 17, 69)
( 18, 70)( 19, 71)( 20, 72)( 21, 73)( 22, 74)( 23, 75)( 24, 76)( 25, 77)
( 26, 78)( 27, 79)( 28, 80)( 29,120)( 30,121)( 31,122)( 32,123)( 33,124)
( 34,125)( 35,126)( 36,127)( 37,128)( 38,129)( 39,130)( 40,131)( 41,132)
( 42,107)( 43,108)( 44,109)( 45,110)( 46,111)( 47,112)( 48,113)( 49,114)
( 50,115)( 51,116)( 52,117)( 53,118)( 54,119)( 55, 94)( 56, 95)( 57, 96)
( 58, 97)( 59, 98)( 60, 99)( 61,100)( 62,101)( 63,102)( 64,103)( 65,104)
( 66,105)( 67,106);
poly := sub<Sym(132)|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, s1*s2*s3*s2*s1*s2*s3*s2, 
s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*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*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