Polytope of Type {26,14}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {26,14}*728
Also Known As : {26,14|2}. if this polytope has another name.
Group : SmallGroup(728,36)
Rank : 3
Schlafli Type : {26,14}
Number of vertices, edges, etc : 26, 182, 14
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 :
   {26,14,2} of size 1456
Vertex Figure Of :
   {2,26,14} of size 1456
Quotients (Maximal Quotients in Boldface) :
   7-fold quotients : {26,2}*104
   13-fold quotients : {2,14}*56
   14-fold quotients : {13,2}*52
   26-fold quotients : {2,7}*28
   91-fold quotients : {2,2}*8
Covers (Minimal Covers in Boldface) :
   2-fold covers : {26,28}*1456, {52,14}*1456
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)(132,143)(133,142)(134,141)(135,140)
(136,139)(137,138)(145,156)(146,155)(147,154)(148,153)(149,152)(150,151)
(158,169)(159,168)(160,167)(161,166)(162,165)(163,164)(171,182)(172,181)
(173,180)(174,179)(175,178)(176,177);;
s1 := (  1,  2)(  3, 13)(  4, 12)(  5, 11)(  6, 10)(  7,  9)( 14, 80)( 15, 79)
( 16, 91)( 17, 90)( 18, 89)( 19, 88)( 20, 87)( 21, 86)( 22, 85)( 23, 84)
( 24, 83)( 25, 82)( 26, 81)( 27, 67)( 28, 66)( 29, 78)( 30, 77)( 31, 76)
( 32, 75)( 33, 74)( 34, 73)( 35, 72)( 36, 71)( 37, 70)( 38, 69)( 39, 68)
( 40, 54)( 41, 53)( 42, 65)( 43, 64)( 44, 63)( 45, 62)( 46, 61)( 47, 60)
( 48, 59)( 49, 58)( 50, 57)( 51, 56)( 52, 55)( 92, 93)( 94,104)( 95,103)
( 96,102)( 97,101)( 98,100)(105,171)(106,170)(107,182)(108,181)(109,180)
(110,179)(111,178)(112,177)(113,176)(114,175)(115,174)(116,173)(117,172)
(118,158)(119,157)(120,169)(121,168)(122,167)(123,166)(124,165)(125,164)
(126,163)(127,162)(128,161)(129,160)(130,159)(131,145)(132,144)(133,156)
(134,155)(135,154)(136,153)(137,152)(138,151)(139,150)(140,149)(141,148)
(142,147)(143,146);;
s2 := (  1,105)(  2,106)(  3,107)(  4,108)(  5,109)(  6,110)(  7,111)(  8,112)
(  9,113)( 10,114)( 11,115)( 12,116)( 13,117)( 14, 92)( 15, 93)( 16, 94)
( 17, 95)( 18, 96)( 19, 97)( 20, 98)( 21, 99)( 22,100)( 23,101)( 24,102)
( 25,103)( 26,104)( 27,170)( 28,171)( 29,172)( 30,173)( 31,174)( 32,175)
( 33,176)( 34,177)( 35,178)( 36,179)( 37,180)( 38,181)( 39,182)( 40,157)
( 41,158)( 42,159)( 43,160)( 44,161)( 45,162)( 46,163)( 47,164)( 48,165)
( 49,166)( 50,167)( 51,168)( 52,169)( 53,144)( 54,145)( 55,146)( 56,147)
( 57,148)( 58,149)( 59,150)( 60,151)( 61,152)( 62,153)( 63,154)( 64,155)
( 65,156)( 66,131)( 67,132)( 68,133)( 69,134)( 70,135)( 71,136)( 72,137)
( 73,138)( 74,139)( 75,140)( 76,141)( 77,142)( 78,143)( 79,118)( 80,119)
( 81,120)( 82,121)( 83,122)( 84,123)( 85,124)( 86,125)( 87,126)( 88,127)
( 89,128)( 90,129)( 91,130);;
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*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(182)!(  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)(132,143)(133,142)(134,141)
(135,140)(136,139)(137,138)(145,156)(146,155)(147,154)(148,153)(149,152)
(150,151)(158,169)(159,168)(160,167)(161,166)(162,165)(163,164)(171,182)
(172,181)(173,180)(174,179)(175,178)(176,177);
s1 := Sym(182)!(  1,  2)(  3, 13)(  4, 12)(  5, 11)(  6, 10)(  7,  9)( 14, 80)
( 15, 79)( 16, 91)( 17, 90)( 18, 89)( 19, 88)( 20, 87)( 21, 86)( 22, 85)
( 23, 84)( 24, 83)( 25, 82)( 26, 81)( 27, 67)( 28, 66)( 29, 78)( 30, 77)
( 31, 76)( 32, 75)( 33, 74)( 34, 73)( 35, 72)( 36, 71)( 37, 70)( 38, 69)
( 39, 68)( 40, 54)( 41, 53)( 42, 65)( 43, 64)( 44, 63)( 45, 62)( 46, 61)
( 47, 60)( 48, 59)( 49, 58)( 50, 57)( 51, 56)( 52, 55)( 92, 93)( 94,104)
( 95,103)( 96,102)( 97,101)( 98,100)(105,171)(106,170)(107,182)(108,181)
(109,180)(110,179)(111,178)(112,177)(113,176)(114,175)(115,174)(116,173)
(117,172)(118,158)(119,157)(120,169)(121,168)(122,167)(123,166)(124,165)
(125,164)(126,163)(127,162)(128,161)(129,160)(130,159)(131,145)(132,144)
(133,156)(134,155)(135,154)(136,153)(137,152)(138,151)(139,150)(140,149)
(141,148)(142,147)(143,146);
s2 := Sym(182)!(  1,105)(  2,106)(  3,107)(  4,108)(  5,109)(  6,110)(  7,111)
(  8,112)(  9,113)( 10,114)( 11,115)( 12,116)( 13,117)( 14, 92)( 15, 93)
( 16, 94)( 17, 95)( 18, 96)( 19, 97)( 20, 98)( 21, 99)( 22,100)( 23,101)
( 24,102)( 25,103)( 26,104)( 27,170)( 28,171)( 29,172)( 30,173)( 31,174)
( 32,175)( 33,176)( 34,177)( 35,178)( 36,179)( 37,180)( 38,181)( 39,182)
( 40,157)( 41,158)( 42,159)( 43,160)( 44,161)( 45,162)( 46,163)( 47,164)
( 48,165)( 49,166)( 50,167)( 51,168)( 52,169)( 53,144)( 54,145)( 55,146)
( 56,147)( 57,148)( 58,149)( 59,150)( 60,151)( 61,152)( 62,153)( 63,154)
( 64,155)( 65,156)( 66,131)( 67,132)( 68,133)( 69,134)( 70,135)( 71,136)
( 72,137)( 73,138)( 74,139)( 75,140)( 76,141)( 77,142)( 78,143)( 79,118)
( 80,119)( 81,120)( 82,121)( 83,122)( 84,123)( 85,124)( 86,125)( 87,126)
( 88,127)( 89,128)( 90,129)( 91,130);
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, 
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, 
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.
to this polytope