Polytope of Type {26,10}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {26,10}*520
Also Known As : {26,10|2}. if this polytope has another name.
Group : SmallGroup(520,45)
Rank : 3
Schlafli Type : {26,10}
Number of vertices, edges, etc : 26, 130, 10
Order of s₀s₁s₂ : 130
Order of s₀s₁s₂s₁ : 2
Special Properties :
   Compact Hyperbolic Quotient
   Locally Spherical
   Orientable
   Flat
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   {26,10,2} of size 1040
Vertex Figure Of :
   {2,26,10} of size 1040
Quotients (Maximal Quotients in Boldface) :
   5-fold quotients : {26,2}*104
   10-fold quotients : {13,2}*52
   13-fold quotients : {2,10}*40
   26-fold quotients : {2,5}*20
   65-fold quotients : {2,2}*8
Covers (Minimal Covers in Boldface) :
   2-fold covers : {26,20}*1040, {52,10}*1040
   3-fold covers : {26,30}*1560, {78,10}*1560
Permutation Representation (GAP) :

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

Finitely Presented Group Representation (GAP) :

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

Permutation Representation (Magma) :

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

Finitely Presented Group Representation (Magma) :

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

References : None.
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