Polytope of Type {182,2}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {182,2}*728
if this polytope has a name.
Group : SmallGroup(728,39)
Rank : 3
Schlafli Type : {182,2}
Number of vertices, edges, etc : 182, 182, 2
Order of s0s1s2 : 182
Order of s0s1s2s1 : 2
Special Properties :
Degenerate
Universal
Compact Hyperbolic Quotient
Locally Spherical
Orientable
Flat
Self-Petrie
Related Polytopes :
Facet
Vertex Figure
Dual
Petrial
Facet Of :
{182,2,2} of size 1456
Vertex Figure Of :
{2,182,2} of size 1456
Quotients (Maximal Quotients in Boldface) :
2-fold quotients : {91,2}*364
7-fold quotients : {26,2}*104
13-fold quotients : {14,2}*56
14-fold quotients : {13,2}*52
26-fold quotients : {7,2}*28
91-fold quotients : {2,2}*8
Covers (Minimal Covers in Boldface) :
2-fold covers : {364,2}*1456, {182,4}*1456
Permutation Representation (GAP) :
s0 := ( 2, 13)( 3, 12)( 4, 11)( 5, 10)( 6, 9)( 7, 8)( 14, 79)( 15, 91)
( 16, 90)( 17, 89)( 18, 88)( 19, 87)( 20, 86)( 21, 85)( 22, 84)( 23, 83)
( 24, 82)( 25, 81)( 26, 80)( 27, 66)( 28, 78)( 29, 77)( 30, 76)( 31, 75)
( 32, 74)( 33, 73)( 34, 72)( 35, 71)( 36, 70)( 37, 69)( 38, 68)( 39, 67)
( 40, 53)( 41, 65)( 42, 64)( 43, 63)( 44, 62)( 45, 61)( 46, 60)( 47, 59)
( 48, 58)( 49, 57)( 50, 56)( 51, 55)( 52, 54)( 93,104)( 94,103)( 95,102)
( 96,101)( 97,100)( 98, 99)(105,170)(106,182)(107,181)(108,180)(109,179)
(110,178)(111,177)(112,176)(113,175)(114,174)(115,173)(116,172)(117,171)
(118,157)(119,169)(120,168)(121,167)(122,166)(123,165)(124,164)(125,163)
(126,162)(127,161)(128,160)(129,159)(130,158)(131,144)(132,156)(133,155)
(134,154)(135,153)(136,152)(137,151)(138,150)(139,149)(140,148)(141,147)
(142,146)(143,145);;
s1 := ( 1,106)( 2,105)( 3,117)( 4,116)( 5,115)( 6,114)( 7,113)( 8,112)
( 9,111)( 10,110)( 11,109)( 12,108)( 13,107)( 14, 93)( 15, 92)( 16,104)
( 17,103)( 18,102)( 19,101)( 20,100)( 21, 99)( 22, 98)( 23, 97)( 24, 96)
( 25, 95)( 26, 94)( 27,171)( 28,170)( 29,182)( 30,181)( 31,180)( 32,179)
( 33,178)( 34,177)( 35,176)( 36,175)( 37,174)( 38,173)( 39,172)( 40,158)
( 41,157)( 42,169)( 43,168)( 44,167)( 45,166)( 46,165)( 47,164)( 48,163)
( 49,162)( 50,161)( 51,160)( 52,159)( 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)( 66,132)( 67,131)( 68,143)( 69,142)( 70,141)( 71,140)( 72,139)
( 73,138)( 74,137)( 75,136)( 76,135)( 77,134)( 78,133)( 79,119)( 80,118)
( 81,130)( 82,129)( 83,128)( 84,127)( 85,126)( 86,125)( 87,124)( 88,123)
( 89,122)( 90,121)( 91,120);;
s2 := (183,184);;
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, 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*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*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*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*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*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*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(184)!( 2, 13)( 3, 12)( 4, 11)( 5, 10)( 6, 9)( 7, 8)( 14, 79)
( 15, 91)( 16, 90)( 17, 89)( 18, 88)( 19, 87)( 20, 86)( 21, 85)( 22, 84)
( 23, 83)( 24, 82)( 25, 81)( 26, 80)( 27, 66)( 28, 78)( 29, 77)( 30, 76)
( 31, 75)( 32, 74)( 33, 73)( 34, 72)( 35, 71)( 36, 70)( 37, 69)( 38, 68)
( 39, 67)( 40, 53)( 41, 65)( 42, 64)( 43, 63)( 44, 62)( 45, 61)( 46, 60)
( 47, 59)( 48, 58)( 49, 57)( 50, 56)( 51, 55)( 52, 54)( 93,104)( 94,103)
( 95,102)( 96,101)( 97,100)( 98, 99)(105,170)(106,182)(107,181)(108,180)
(109,179)(110,178)(111,177)(112,176)(113,175)(114,174)(115,173)(116,172)
(117,171)(118,157)(119,169)(120,168)(121,167)(122,166)(123,165)(124,164)
(125,163)(126,162)(127,161)(128,160)(129,159)(130,158)(131,144)(132,156)
(133,155)(134,154)(135,153)(136,152)(137,151)(138,150)(139,149)(140,148)
(141,147)(142,146)(143,145);
s1 := Sym(184)!( 1,106)( 2,105)( 3,117)( 4,116)( 5,115)( 6,114)( 7,113)
( 8,112)( 9,111)( 10,110)( 11,109)( 12,108)( 13,107)( 14, 93)( 15, 92)
( 16,104)( 17,103)( 18,102)( 19,101)( 20,100)( 21, 99)( 22, 98)( 23, 97)
( 24, 96)( 25, 95)( 26, 94)( 27,171)( 28,170)( 29,182)( 30,181)( 31,180)
( 32,179)( 33,178)( 34,177)( 35,176)( 36,175)( 37,174)( 38,173)( 39,172)
( 40,158)( 41,157)( 42,169)( 43,168)( 44,167)( 45,166)( 46,165)( 47,164)
( 48,163)( 49,162)( 50,161)( 51,160)( 52,159)( 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)( 66,132)( 67,131)( 68,143)( 69,142)( 70,141)( 71,140)
( 72,139)( 73,138)( 74,137)( 75,136)( 76,135)( 77,134)( 78,133)( 79,119)
( 80,118)( 81,130)( 82,129)( 83,128)( 84,127)( 85,126)( 86,125)( 87,124)
( 88,123)( 89,122)( 90,121)( 91,120);
s2 := Sym(184)!(183,184);
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*s2*s0*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*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*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*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*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*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*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 >;
to this polytope