Polytope of Type {6,92}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {6,92}*1656
if this polytope has a name.
Group : SmallGroup(1656,113)
Rank : 3
Schlafli Type : {6,92}
Number of vertices, edges, etc : 9, 414, 138
Order of s₀s₁s₂ : 92
Order of s₀s₁s₂s₁ : 6
Special Properties :
   Compact Hyperbolic Quotient
   Locally Spherical
   Non-Orientable
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   None in this Atlas
Vertex Figure Of :
   None in this Atlas
Quotients (Maximal Quotients in Boldface) :
   23-fold quotients : {6,4}*72
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :

s0 := ( 24, 47)( 25, 48)( 26, 49)( 27, 50)( 28, 51)( 29, 52)( 30, 53)( 31, 54)
( 32, 55)( 33, 56)( 34, 57)( 35, 58)( 36, 59)( 37, 60)( 38, 61)( 39, 62)
( 40, 63)( 41, 64)( 42, 65)( 43, 66)( 44, 67)( 45, 68)( 46, 69)( 70,139)
( 71,140)( 72,141)( 73,142)( 74,143)( 75,144)( 76,145)( 77,146)( 78,147)
( 79,148)( 80,149)( 81,150)( 82,151)( 83,152)( 84,153)( 85,154)( 86,155)
( 87,156)( 88,157)( 89,158)( 90,159)( 91,160)( 92,161)( 93,185)( 94,186)
( 95,187)( 96,188)( 97,189)( 98,190)( 99,191)(100,192)(101,193)(102,194)
(103,195)(104,196)(105,197)(106,198)(107,199)(108,200)(109,201)(110,202)
(111,203)(112,204)(113,205)(114,206)(115,207)(116,162)(117,163)(118,164)
(119,165)(120,166)(121,167)(122,168)(123,169)(124,170)(125,171)(126,172)
(127,173)(128,174)(129,175)(130,176)(131,177)(132,178)(133,179)(134,180)
(135,181)(136,182)(137,183)(138,184);;
s1 := (  1, 70)(  2, 92)(  3, 91)(  4, 90)(  5, 89)(  6, 88)(  7, 87)(  8, 86)
(  9, 85)( 10, 84)( 11, 83)( 12, 82)( 13, 81)( 14, 80)( 15, 79)( 16, 78)
( 17, 77)( 18, 76)( 19, 75)( 20, 74)( 21, 73)( 22, 72)( 23, 71)( 24, 93)
( 25,115)( 26,114)( 27,113)( 28,112)( 29,111)( 30,110)( 31,109)( 32,108)
( 33,107)( 34,106)( 35,105)( 36,104)( 37,103)( 38,102)( 39,101)( 40,100)
( 41, 99)( 42, 98)( 43, 97)( 44, 96)( 45, 95)( 46, 94)( 47,116)( 48,138)
( 49,137)( 50,136)( 51,135)( 52,134)( 53,133)( 54,132)( 55,131)( 56,130)
( 57,129)( 58,128)( 59,127)( 60,126)( 61,125)( 62,124)( 63,123)( 64,122)
( 65,121)( 66,120)( 67,119)( 68,118)( 69,117)(140,161)(141,160)(142,159)
(143,158)(144,157)(145,156)(146,155)(147,154)(148,153)(149,152)(150,151)
(163,184)(164,183)(165,182)(166,181)(167,180)(168,179)(169,178)(170,177)
(171,176)(172,175)(173,174)(186,207)(187,206)(188,205)(189,204)(190,203)
(191,202)(192,201)(193,200)(194,199)(195,198)(196,197);;
s2 := (  1,  2)(  3, 23)(  4, 22)(  5, 21)(  6, 20)(  7, 19)(  8, 18)(  9, 17)
( 10, 16)( 11, 15)( 12, 14)( 24, 71)( 25, 70)( 26, 92)( 27, 91)( 28, 90)
( 29, 89)( 30, 88)( 31, 87)( 32, 86)( 33, 85)( 34, 84)( 35, 83)( 36, 82)
( 37, 81)( 38, 80)( 39, 79)( 40, 78)( 41, 77)( 42, 76)( 43, 75)( 44, 74)
( 45, 73)( 46, 72)( 47,140)( 48,139)( 49,161)( 50,160)( 51,159)( 52,158)
( 53,157)( 54,156)( 55,155)( 56,154)( 57,153)( 58,152)( 59,151)( 60,150)
( 61,149)( 62,148)( 63,147)( 64,146)( 65,145)( 66,144)( 67,143)( 68,142)
( 69,141)( 93, 94)( 95,115)( 96,114)( 97,113)( 98,112)( 99,111)(100,110)
(101,109)(102,108)(103,107)(104,106)(116,163)(117,162)(118,184)(119,183)
(120,182)(121,181)(122,180)(123,179)(124,178)(125,177)(126,176)(127,175)
(128,174)(129,173)(130,172)(131,171)(132,170)(133,169)(134,168)(135,167)
(136,166)(137,165)(138,164)(185,186)(187,207)(188,206)(189,205)(190,204)
(191,203)(192,202)(193,201)(194,200)(195,199)(196,198);;
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*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1, 
s2*s0*s1*s2*s0*s1*s0*s1*s2*s1*s2*s1*s0*s1, 
s0*s1*s2*s1*s2*s0*s1*s2*s1*s2*s0*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*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(207)!( 24, 47)( 25, 48)( 26, 49)( 27, 50)( 28, 51)( 29, 52)( 30, 53)
( 31, 54)( 32, 55)( 33, 56)( 34, 57)( 35, 58)( 36, 59)( 37, 60)( 38, 61)
( 39, 62)( 40, 63)( 41, 64)( 42, 65)( 43, 66)( 44, 67)( 45, 68)( 46, 69)
( 70,139)( 71,140)( 72,141)( 73,142)( 74,143)( 75,144)( 76,145)( 77,146)
( 78,147)( 79,148)( 80,149)( 81,150)( 82,151)( 83,152)( 84,153)( 85,154)
( 86,155)( 87,156)( 88,157)( 89,158)( 90,159)( 91,160)( 92,161)( 93,185)
( 94,186)( 95,187)( 96,188)( 97,189)( 98,190)( 99,191)(100,192)(101,193)
(102,194)(103,195)(104,196)(105,197)(106,198)(107,199)(108,200)(109,201)
(110,202)(111,203)(112,204)(113,205)(114,206)(115,207)(116,162)(117,163)
(118,164)(119,165)(120,166)(121,167)(122,168)(123,169)(124,170)(125,171)
(126,172)(127,173)(128,174)(129,175)(130,176)(131,177)(132,178)(133,179)
(134,180)(135,181)(136,182)(137,183)(138,184);
s1 := Sym(207)!(  1, 70)(  2, 92)(  3, 91)(  4, 90)(  5, 89)(  6, 88)(  7, 87)
(  8, 86)(  9, 85)( 10, 84)( 11, 83)( 12, 82)( 13, 81)( 14, 80)( 15, 79)
( 16, 78)( 17, 77)( 18, 76)( 19, 75)( 20, 74)( 21, 73)( 22, 72)( 23, 71)
( 24, 93)( 25,115)( 26,114)( 27,113)( 28,112)( 29,111)( 30,110)( 31,109)
( 32,108)( 33,107)( 34,106)( 35,105)( 36,104)( 37,103)( 38,102)( 39,101)
( 40,100)( 41, 99)( 42, 98)( 43, 97)( 44, 96)( 45, 95)( 46, 94)( 47,116)
( 48,138)( 49,137)( 50,136)( 51,135)( 52,134)( 53,133)( 54,132)( 55,131)
( 56,130)( 57,129)( 58,128)( 59,127)( 60,126)( 61,125)( 62,124)( 63,123)
( 64,122)( 65,121)( 66,120)( 67,119)( 68,118)( 69,117)(140,161)(141,160)
(142,159)(143,158)(144,157)(145,156)(146,155)(147,154)(148,153)(149,152)
(150,151)(163,184)(164,183)(165,182)(166,181)(167,180)(168,179)(169,178)
(170,177)(171,176)(172,175)(173,174)(186,207)(187,206)(188,205)(189,204)
(190,203)(191,202)(192,201)(193,200)(194,199)(195,198)(196,197);
s2 := Sym(207)!(  1,  2)(  3, 23)(  4, 22)(  5, 21)(  6, 20)(  7, 19)(  8, 18)
(  9, 17)( 10, 16)( 11, 15)( 12, 14)( 24, 71)( 25, 70)( 26, 92)( 27, 91)
( 28, 90)( 29, 89)( 30, 88)( 31, 87)( 32, 86)( 33, 85)( 34, 84)( 35, 83)
( 36, 82)( 37, 81)( 38, 80)( 39, 79)( 40, 78)( 41, 77)( 42, 76)( 43, 75)
( 44, 74)( 45, 73)( 46, 72)( 47,140)( 48,139)( 49,161)( 50,160)( 51,159)
( 52,158)( 53,157)( 54,156)( 55,155)( 56,154)( 57,153)( 58,152)( 59,151)
( 60,150)( 61,149)( 62,148)( 63,147)( 64,146)( 65,145)( 66,144)( 67,143)
( 68,142)( 69,141)( 93, 94)( 95,115)( 96,114)( 97,113)( 98,112)( 99,111)
(100,110)(101,109)(102,108)(103,107)(104,106)(116,163)(117,162)(118,184)
(119,183)(120,182)(121,181)(122,180)(123,179)(124,178)(125,177)(126,176)
(127,175)(128,174)(129,173)(130,172)(131,171)(132,170)(133,169)(134,168)
(135,167)(136,166)(137,165)(138,164)(185,186)(187,207)(188,206)(189,205)
(190,204)(191,203)(192,202)(193,201)(194,200)(195,199)(196,198);
poly := sub<Sym(207)|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*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1, 
s2*s0*s1*s2*s0*s1*s0*s1*s2*s1*s2*s1*s0*s1, 
s0*s1*s2*s1*s2*s0*s1*s2*s1*s2*s0*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2 >;

References : None.
to this polytope