Polytope of Type {2,182}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,182}*728
if this polytope has a name.
Group : SmallGroup(728,39)
Rank : 3
Schlafli Type : {2,182}
Number of vertices, edges, etc : 2, 182, 182
Order of s₀s₁s₂ : 182
Order of s₀s₁s₂s₁ : 2
Special Properties :
   Degenerate
   Universal
   Compact Hyperbolic Quotient
   Locally Spherical
   Orientable
   Flat
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   {2,182,2} of size 1456
Vertex Figure Of :
   {2,2,182} of size 1456
Quotients (Maximal Quotients in Boldface) :
   2-fold quotients : {2,91}*364
   7-fold quotients : {2,26}*104
   13-fold quotients : {2,14}*56
   14-fold quotients : {2,13}*52
   26-fold quotients : {2,7}*28
   91-fold quotients : {2,2}*8
Covers (Minimal Covers in Boldface) :
   2-fold covers : {2,364}*1456, {4,182}*1456
Permutation Representation (GAP) :

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

Finitely Presented Group Representation (Magma) :

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

to this polytope