Polytope of Type {2,26,14}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,26,14}*1456
if this polytope has a name.
Group : SmallGroup(1456,175)
Rank : 4
Schlafli Type : {2,26,14}
Number of vertices, edges, etc : 2, 26, 182, 14
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 : {2,26,2}*208
   13-fold quotients : {2,2,14}*112
   14-fold quotients : {2,13,2}*104
   26-fold quotients : {2,2,7}*56
   91-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)(134,145)(135,144)(136,143)(137,142)
(138,141)(139,140)(147,158)(148,157)(149,156)(150,155)(151,154)(152,153)
(160,171)(161,170)(162,169)(163,168)(164,167)(165,166)(173,184)(174,183)
(175,182)(176,181)(177,180)(178,179);;
s2 := (  3,  4)(  5, 15)(  6, 14)(  7, 13)(  8, 12)(  9, 11)( 16, 82)( 17, 81)
( 18, 93)( 19, 92)( 20, 91)( 21, 90)( 22, 89)( 23, 88)( 24, 87)( 25, 86)
( 26, 85)( 27, 84)( 28, 83)( 29, 69)( 30, 68)( 31, 80)( 32, 79)( 33, 78)
( 34, 77)( 35, 76)( 36, 75)( 37, 74)( 38, 73)( 39, 72)( 40, 71)( 41, 70)
( 42, 56)( 43, 55)( 44, 67)( 45, 66)( 46, 65)( 47, 64)( 48, 63)( 49, 62)
( 50, 61)( 51, 60)( 52, 59)( 53, 58)( 54, 57)( 94, 95)( 96,106)( 97,105)
( 98,104)( 99,103)(100,102)(107,173)(108,172)(109,184)(110,183)(111,182)
(112,181)(113,180)(114,179)(115,178)(116,177)(117,176)(118,175)(119,174)
(120,160)(121,159)(122,171)(123,170)(124,169)(125,168)(126,167)(127,166)
(128,165)(129,164)(130,163)(131,162)(132,161)(133,147)(134,146)(135,158)
(136,157)(137,156)(138,155)(139,154)(140,153)(141,152)(142,151)(143,150)
(144,149)(145,148);;
s3 := (  3,107)(  4,108)(  5,109)(  6,110)(  7,111)(  8,112)(  9,113)( 10,114)
( 11,115)( 12,116)( 13,117)( 14,118)( 15,119)( 16, 94)( 17, 95)( 18, 96)
( 19, 97)( 20, 98)( 21, 99)( 22,100)( 23,101)( 24,102)( 25,103)( 26,104)
( 27,105)( 28,106)( 29,172)( 30,173)( 31,174)( 32,175)( 33,176)( 34,177)
( 35,178)( 36,179)( 37,180)( 38,181)( 39,182)( 40,183)( 41,184)( 42,159)
( 43,160)( 44,161)( 45,162)( 46,163)( 47,164)( 48,165)( 49,166)( 50,167)
( 51,168)( 52,169)( 53,170)( 54,171)( 55,146)( 56,147)( 57,148)( 58,149)
( 59,150)( 60,151)( 61,152)( 62,153)( 63,154)( 64,155)( 65,156)( 66,157)
( 67,158)( 68,133)( 69,134)( 70,135)( 71,136)( 72,137)( 73,138)( 74,139)
( 75,140)( 76,141)( 77,142)( 78,143)( 79,144)( 80,145)( 81,120)( 82,121)
( 83,122)( 84,123)( 85,124)( 86,125)( 87,126)( 88,127)( 89,128)( 90,129)
( 91,130)( 92,131)( 93,132);;
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*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(184)!(1,2);
s1 := Sym(184)!(  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)(134,145)(135,144)(136,143)
(137,142)(138,141)(139,140)(147,158)(148,157)(149,156)(150,155)(151,154)
(152,153)(160,171)(161,170)(162,169)(163,168)(164,167)(165,166)(173,184)
(174,183)(175,182)(176,181)(177,180)(178,179);
s2 := Sym(184)!(  3,  4)(  5, 15)(  6, 14)(  7, 13)(  8, 12)(  9, 11)( 16, 82)
( 17, 81)( 18, 93)( 19, 92)( 20, 91)( 21, 90)( 22, 89)( 23, 88)( 24, 87)
( 25, 86)( 26, 85)( 27, 84)( 28, 83)( 29, 69)( 30, 68)( 31, 80)( 32, 79)
( 33, 78)( 34, 77)( 35, 76)( 36, 75)( 37, 74)( 38, 73)( 39, 72)( 40, 71)
( 41, 70)( 42, 56)( 43, 55)( 44, 67)( 45, 66)( 46, 65)( 47, 64)( 48, 63)
( 49, 62)( 50, 61)( 51, 60)( 52, 59)( 53, 58)( 54, 57)( 94, 95)( 96,106)
( 97,105)( 98,104)( 99,103)(100,102)(107,173)(108,172)(109,184)(110,183)
(111,182)(112,181)(113,180)(114,179)(115,178)(116,177)(117,176)(118,175)
(119,174)(120,160)(121,159)(122,171)(123,170)(124,169)(125,168)(126,167)
(127,166)(128,165)(129,164)(130,163)(131,162)(132,161)(133,147)(134,146)
(135,158)(136,157)(137,156)(138,155)(139,154)(140,153)(141,152)(142,151)
(143,150)(144,149)(145,148);
s3 := Sym(184)!(  3,107)(  4,108)(  5,109)(  6,110)(  7,111)(  8,112)(  9,113)
( 10,114)( 11,115)( 12,116)( 13,117)( 14,118)( 15,119)( 16, 94)( 17, 95)
( 18, 96)( 19, 97)( 20, 98)( 21, 99)( 22,100)( 23,101)( 24,102)( 25,103)
( 26,104)( 27,105)( 28,106)( 29,172)( 30,173)( 31,174)( 32,175)( 33,176)
( 34,177)( 35,178)( 36,179)( 37,180)( 38,181)( 39,182)( 40,183)( 41,184)
( 42,159)( 43,160)( 44,161)( 45,162)( 46,163)( 47,164)( 48,165)( 49,166)
( 50,167)( 51,168)( 52,169)( 53,170)( 54,171)( 55,146)( 56,147)( 57,148)
( 58,149)( 59,150)( 60,151)( 61,152)( 62,153)( 63,154)( 64,155)( 65,156)
( 66,157)( 67,158)( 68,133)( 69,134)( 70,135)( 71,136)( 72,137)( 73,138)
( 74,139)( 75,140)( 76,141)( 77,142)( 78,143)( 79,144)( 80,145)( 81,120)
( 82,121)( 83,122)( 84,123)( 85,124)( 86,125)( 87,126)( 88,127)( 89,128)
( 90,129)( 91,130)( 92,131)( 93,132);
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, 
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, 
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