Polytope of Type {2,14,26}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,14,26}*1456
if this polytope has a name.
Group : SmallGroup(1456,175)
Rank : 4
Schlafli Type : {2,14,26}
Number of vertices, edges, etc : 2, 14, 182, 26
Order of s₀s₁s₂s₃ : 182
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) :
   7-fold quotients : {2,2,26}*208
   13-fold quotients : {2,14,2}*112
   14-fold quotients : {2,2,13}*104
   26-fold quotients : {2,7,2}*56
   91-fold quotients : {2,2,2}*16
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :

s0 := (1,2);;
s1 := ( 16, 81)( 17, 82)( 18, 83)( 19, 84)( 20, 85)( 21, 86)( 22, 87)( 23, 88)
( 24, 89)( 25, 90)( 26, 91)( 27, 92)( 28, 93)( 29, 68)( 30, 69)( 31, 70)
( 32, 71)( 33, 72)( 34, 73)( 35, 74)( 36, 75)( 37, 76)( 38, 77)( 39, 78)
( 40, 79)( 41, 80)( 42, 55)( 43, 56)( 44, 57)( 45, 58)( 46, 59)( 47, 60)
( 48, 61)( 49, 62)( 50, 63)( 51, 64)( 52, 65)( 53, 66)( 54, 67)(107,172)
(108,173)(109,174)(110,175)(111,176)(112,177)(113,178)(114,179)(115,180)
(116,181)(117,182)(118,183)(119,184)(120,159)(121,160)(122,161)(123,162)
(124,163)(125,164)(126,165)(127,166)(128,167)(129,168)(130,169)(131,170)
(132,171)(133,146)(134,147)(135,148)(136,149)(137,150)(138,151)(139,152)
(140,153)(141,154)(142,155)(143,156)(144,157)(145,158);;
s2 := (  3, 16)(  4, 28)(  5, 27)(  6, 26)(  7, 25)(  8, 24)(  9, 23)( 10, 22)
( 11, 21)( 12, 20)( 13, 19)( 14, 18)( 15, 17)( 29, 81)( 30, 93)( 31, 92)
( 32, 91)( 33, 90)( 34, 89)( 35, 88)( 36, 87)( 37, 86)( 38, 85)( 39, 84)
( 40, 83)( 41, 82)( 42, 68)( 43, 80)( 44, 79)( 45, 78)( 46, 77)( 47, 76)
( 48, 75)( 49, 74)( 50, 73)( 51, 72)( 52, 71)( 53, 70)( 54, 69)( 56, 67)
( 57, 66)( 58, 65)( 59, 64)( 60, 63)( 61, 62)( 94,107)( 95,119)( 96,118)
( 97,117)( 98,116)( 99,115)(100,114)(101,113)(102,112)(103,111)(104,110)
(105,109)(106,108)(120,172)(121,184)(122,183)(123,182)(124,181)(125,180)
(126,179)(127,178)(128,177)(129,176)(130,175)(131,174)(132,173)(133,159)
(134,171)(135,170)(136,169)(137,168)(138,167)(139,166)(140,165)(141,164)
(142,163)(143,162)(144,161)(145,160)(147,158)(148,157)(149,156)(150,155)
(151,154)(152,153);;
s3 := (  3, 95)(  4, 94)(  5,106)(  6,105)(  7,104)(  8,103)(  9,102)( 10,101)
( 11,100)( 12, 99)( 13, 98)( 14, 97)( 15, 96)( 16,108)( 17,107)( 18,119)
( 19,118)( 20,117)( 21,116)( 22,115)( 23,114)( 24,113)( 25,112)( 26,111)
( 27,110)( 28,109)( 29,121)( 30,120)( 31,132)( 32,131)( 33,130)( 34,129)
( 35,128)( 36,127)( 37,126)( 38,125)( 39,124)( 40,123)( 41,122)( 42,134)
( 43,133)( 44,145)( 45,144)( 46,143)( 47,142)( 48,141)( 49,140)( 50,139)
( 51,138)( 52,137)( 53,136)( 54,135)( 55,147)( 56,146)( 57,158)( 58,157)
( 59,156)( 60,155)( 61,154)( 62,153)( 63,152)( 64,151)( 65,150)( 66,149)
( 67,148)( 68,160)( 69,159)( 70,171)( 71,170)( 72,169)( 73,168)( 74,167)
( 75,166)( 76,165)( 77,164)( 78,163)( 79,162)( 80,161)( 81,173)( 82,172)
( 83,184)( 84,183)( 85,182)( 86,181)( 87,180)( 88,179)( 89,178)( 90,177)
( 91,176)( 92,175)( 93,174);;
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, 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, 
s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3 ];;
poly := F / rels;;

Permutation Representation (Magma) :

s0 := Sym(184)!(1,2);
s1 := Sym(184)!( 16, 81)( 17, 82)( 18, 83)( 19, 84)( 20, 85)( 21, 86)( 22, 87)
( 23, 88)( 24, 89)( 25, 90)( 26, 91)( 27, 92)( 28, 93)( 29, 68)( 30, 69)
( 31, 70)( 32, 71)( 33, 72)( 34, 73)( 35, 74)( 36, 75)( 37, 76)( 38, 77)
( 39, 78)( 40, 79)( 41, 80)( 42, 55)( 43, 56)( 44, 57)( 45, 58)( 46, 59)
( 47, 60)( 48, 61)( 49, 62)( 50, 63)( 51, 64)( 52, 65)( 53, 66)( 54, 67)
(107,172)(108,173)(109,174)(110,175)(111,176)(112,177)(113,178)(114,179)
(115,180)(116,181)(117,182)(118,183)(119,184)(120,159)(121,160)(122,161)
(123,162)(124,163)(125,164)(126,165)(127,166)(128,167)(129,168)(130,169)
(131,170)(132,171)(133,146)(134,147)(135,148)(136,149)(137,150)(138,151)
(139,152)(140,153)(141,154)(142,155)(143,156)(144,157)(145,158);
s2 := Sym(184)!(  3, 16)(  4, 28)(  5, 27)(  6, 26)(  7, 25)(  8, 24)(  9, 23)
( 10, 22)( 11, 21)( 12, 20)( 13, 19)( 14, 18)( 15, 17)( 29, 81)( 30, 93)
( 31, 92)( 32, 91)( 33, 90)( 34, 89)( 35, 88)( 36, 87)( 37, 86)( 38, 85)
( 39, 84)( 40, 83)( 41, 82)( 42, 68)( 43, 80)( 44, 79)( 45, 78)( 46, 77)
( 47, 76)( 48, 75)( 49, 74)( 50, 73)( 51, 72)( 52, 71)( 53, 70)( 54, 69)
( 56, 67)( 57, 66)( 58, 65)( 59, 64)( 60, 63)( 61, 62)( 94,107)( 95,119)
( 96,118)( 97,117)( 98,116)( 99,115)(100,114)(101,113)(102,112)(103,111)
(104,110)(105,109)(106,108)(120,172)(121,184)(122,183)(123,182)(124,181)
(125,180)(126,179)(127,178)(128,177)(129,176)(130,175)(131,174)(132,173)
(133,159)(134,171)(135,170)(136,169)(137,168)(138,167)(139,166)(140,165)
(141,164)(142,163)(143,162)(144,161)(145,160)(147,158)(148,157)(149,156)
(150,155)(151,154)(152,153);
s3 := Sym(184)!(  3, 95)(  4, 94)(  5,106)(  6,105)(  7,104)(  8,103)(  9,102)
( 10,101)( 11,100)( 12, 99)( 13, 98)( 14, 97)( 15, 96)( 16,108)( 17,107)
( 18,119)( 19,118)( 20,117)( 21,116)( 22,115)( 23,114)( 24,113)( 25,112)
( 26,111)( 27,110)( 28,109)( 29,121)( 30,120)( 31,132)( 32,131)( 33,130)
( 34,129)( 35,128)( 36,127)( 37,126)( 38,125)( 39,124)( 40,123)( 41,122)
( 42,134)( 43,133)( 44,145)( 45,144)( 46,143)( 47,142)( 48,141)( 49,140)
( 50,139)( 51,138)( 52,137)( 53,136)( 54,135)( 55,147)( 56,146)( 57,158)
( 58,157)( 59,156)( 60,155)( 61,154)( 62,153)( 63,152)( 64,151)( 65,150)
( 66,149)( 67,148)( 68,160)( 69,159)( 70,171)( 71,170)( 72,169)( 73,168)
( 74,167)( 75,166)( 76,165)( 77,164)( 78,163)( 79,162)( 80,161)( 81,173)
( 82,172)( 83,184)( 84,183)( 85,182)( 86,181)( 87,180)( 88,179)( 89,178)
( 90,177)( 91,176)( 92,175)( 93,174);
poly := sub<Sym(184)|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, 
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, 
s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3 >;

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