Polytope of Type {14,26}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {14,26}*728
Also Known As : {14,26|2}. if this polytope has another name.
Group : SmallGroup(728,36)
Rank : 3
Schlafli Type : {14,26}
Number of vertices, edges, etc : 14, 182, 26
Order of s₀s₁s₂ : 182
Order of s₀s₁s₂s₁ : 2
Special Properties :
   Compact Hyperbolic Quotient
   Locally Spherical
   Orientable
   Flat
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   {14,26,2} of size 1456
Vertex Figure Of :
   {2,14,26} of size 1456
Quotients (Maximal Quotients in Boldface) :
   7-fold quotients : {2,26}*104
   13-fold quotients : {14,2}*56
   14-fold quotients : {2,13}*52
   26-fold quotients : {7,2}*28
   91-fold quotients : {2,2}*8
Covers (Minimal Covers in Boldface) :
   2-fold covers : {28,26}*1456, {14,52}*1456
Permutation Representation (GAP) :

s0 := ( 14, 79)( 15, 80)( 16, 81)( 17, 82)( 18, 83)( 19, 84)( 20, 85)( 21, 86)
( 22, 87)( 23, 88)( 24, 89)( 25, 90)( 26, 91)( 27, 66)( 28, 67)( 29, 68)
( 30, 69)( 31, 70)( 32, 71)( 33, 72)( 34, 73)( 35, 74)( 36, 75)( 37, 76)
( 38, 77)( 39, 78)( 40, 53)( 41, 54)( 42, 55)( 43, 56)( 44, 57)( 45, 58)
( 46, 59)( 47, 60)( 48, 61)( 49, 62)( 50, 63)( 51, 64)( 52, 65)(105,170)
(106,171)(107,172)(108,173)(109,174)(110,175)(111,176)(112,177)(113,178)
(114,179)(115,180)(116,181)(117,182)(118,157)(119,158)(120,159)(121,160)
(122,161)(123,162)(124,163)(125,164)(126,165)(127,166)(128,167)(129,168)
(130,169)(131,144)(132,145)(133,146)(134,147)(135,148)(136,149)(137,150)
(138,151)(139,152)(140,153)(141,154)(142,155)(143,156);;
s1 := (  1, 14)(  2, 26)(  3, 25)(  4, 24)(  5, 23)(  6, 22)(  7, 21)(  8, 20)
(  9, 19)( 10, 18)( 11, 17)( 12, 16)( 13, 15)( 27, 79)( 28, 91)( 29, 90)
( 30, 89)( 31, 88)( 32, 87)( 33, 86)( 34, 85)( 35, 84)( 36, 83)( 37, 82)
( 38, 81)( 39, 80)( 40, 66)( 41, 78)( 42, 77)( 43, 76)( 44, 75)( 45, 74)
( 46, 73)( 47, 72)( 48, 71)( 49, 70)( 50, 69)( 51, 68)( 52, 67)( 54, 65)
( 55, 64)( 56, 63)( 57, 62)( 58, 61)( 59, 60)( 92,105)( 93,117)( 94,116)
( 95,115)( 96,114)( 97,113)( 98,112)( 99,111)(100,110)(101,109)(102,108)
(103,107)(104,106)(118,170)(119,182)(120,181)(121,180)(122,179)(123,178)
(124,177)(125,176)(126,175)(127,174)(128,173)(129,172)(130,171)(131,157)
(132,169)(133,168)(134,167)(135,166)(136,165)(137,164)(138,163)(139,162)
(140,161)(141,160)(142,159)(143,158)(145,156)(146,155)(147,154)(148,153)
(149,152)(150,151);;
s2 := (  1, 93)(  2, 92)(  3,104)(  4,103)(  5,102)(  6,101)(  7,100)(  8, 99)
(  9, 98)( 10, 97)( 11, 96)( 12, 95)( 13, 94)( 14,106)( 15,105)( 16,117)
( 17,116)( 18,115)( 19,114)( 20,113)( 21,112)( 22,111)( 23,110)( 24,109)
( 25,108)( 26,107)( 27,119)( 28,118)( 29,130)( 30,129)( 31,128)( 32,127)
( 33,126)( 34,125)( 35,124)( 36,123)( 37,122)( 38,121)( 39,120)( 40,132)
( 41,131)( 42,143)( 43,142)( 44,141)( 45,140)( 46,139)( 47,138)( 48,137)
( 49,136)( 50,135)( 51,134)( 52,133)( 53,145)( 54,144)( 55,156)( 56,155)
( 57,154)( 58,153)( 59,152)( 60,151)( 61,150)( 62,149)( 63,148)( 64,147)
( 65,146)( 66,158)( 67,157)( 68,169)( 69,168)( 70,167)( 71,166)( 72,165)
( 73,164)( 74,163)( 75,162)( 76,161)( 77,160)( 78,159)( 79,171)( 80,170)
( 81,182)( 82,181)( 83,180)( 84,179)( 85,178)( 86,177)( 87,176)( 88,175)
( 89,174)( 90,173)( 91,172);;
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, 
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, 
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(182)!( 14, 79)( 15, 80)( 16, 81)( 17, 82)( 18, 83)( 19, 84)( 20, 85)
( 21, 86)( 22, 87)( 23, 88)( 24, 89)( 25, 90)( 26, 91)( 27, 66)( 28, 67)
( 29, 68)( 30, 69)( 31, 70)( 32, 71)( 33, 72)( 34, 73)( 35, 74)( 36, 75)
( 37, 76)( 38, 77)( 39, 78)( 40, 53)( 41, 54)( 42, 55)( 43, 56)( 44, 57)
( 45, 58)( 46, 59)( 47, 60)( 48, 61)( 49, 62)( 50, 63)( 51, 64)( 52, 65)
(105,170)(106,171)(107,172)(108,173)(109,174)(110,175)(111,176)(112,177)
(113,178)(114,179)(115,180)(116,181)(117,182)(118,157)(119,158)(120,159)
(121,160)(122,161)(123,162)(124,163)(125,164)(126,165)(127,166)(128,167)
(129,168)(130,169)(131,144)(132,145)(133,146)(134,147)(135,148)(136,149)
(137,150)(138,151)(139,152)(140,153)(141,154)(142,155)(143,156);
s1 := Sym(182)!(  1, 14)(  2, 26)(  3, 25)(  4, 24)(  5, 23)(  6, 22)(  7, 21)
(  8, 20)(  9, 19)( 10, 18)( 11, 17)( 12, 16)( 13, 15)( 27, 79)( 28, 91)
( 29, 90)( 30, 89)( 31, 88)( 32, 87)( 33, 86)( 34, 85)( 35, 84)( 36, 83)
( 37, 82)( 38, 81)( 39, 80)( 40, 66)( 41, 78)( 42, 77)( 43, 76)( 44, 75)
( 45, 74)( 46, 73)( 47, 72)( 48, 71)( 49, 70)( 50, 69)( 51, 68)( 52, 67)
( 54, 65)( 55, 64)( 56, 63)( 57, 62)( 58, 61)( 59, 60)( 92,105)( 93,117)
( 94,116)( 95,115)( 96,114)( 97,113)( 98,112)( 99,111)(100,110)(101,109)
(102,108)(103,107)(104,106)(118,170)(119,182)(120,181)(121,180)(122,179)
(123,178)(124,177)(125,176)(126,175)(127,174)(128,173)(129,172)(130,171)
(131,157)(132,169)(133,168)(134,167)(135,166)(136,165)(137,164)(138,163)
(139,162)(140,161)(141,160)(142,159)(143,158)(145,156)(146,155)(147,154)
(148,153)(149,152)(150,151);
s2 := Sym(182)!(  1, 93)(  2, 92)(  3,104)(  4,103)(  5,102)(  6,101)(  7,100)
(  8, 99)(  9, 98)( 10, 97)( 11, 96)( 12, 95)( 13, 94)( 14,106)( 15,105)
( 16,117)( 17,116)( 18,115)( 19,114)( 20,113)( 21,112)( 22,111)( 23,110)
( 24,109)( 25,108)( 26,107)( 27,119)( 28,118)( 29,130)( 30,129)( 31,128)
( 32,127)( 33,126)( 34,125)( 35,124)( 36,123)( 37,122)( 38,121)( 39,120)
( 40,132)( 41,131)( 42,143)( 43,142)( 44,141)( 45,140)( 46,139)( 47,138)
( 48,137)( 49,136)( 50,135)( 51,134)( 52,133)( 53,145)( 54,144)( 55,156)
( 56,155)( 57,154)( 58,153)( 59,152)( 60,151)( 61,150)( 62,149)( 63,148)
( 64,147)( 65,146)( 66,158)( 67,157)( 68,169)( 69,168)( 70,167)( 71,166)
( 72,165)( 73,164)( 74,163)( 75,162)( 76,161)( 77,160)( 78,159)( 79,171)
( 80,170)( 81,182)( 82,181)( 83,180)( 84,179)( 85,178)( 86,177)( 87,176)
( 88,175)( 89,174)( 90,173)( 91,172);
poly := sub<Sym(182)|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, 
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, 
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 >;

References : None.
to this polytope