Polytope of Type {6,62}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {6,62}*744
Also Known As : {6,62|2}. if this polytope has another name.
Group : SmallGroup(744,47)
Rank : 3
Schlafli Type : {6,62}
Number of vertices, edges, etc : 6, 186, 62
Order of s₀s₁s₂ : 186
Order of s₀s₁s₂s₁ : 2
Special Properties :
   Compact Hyperbolic Quotient
   Locally Spherical
   Orientable
   Flat
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   {6,62,2} of size 1488
Vertex Figure Of :
   {2,6,62} of size 1488
Quotients (Maximal Quotients in Boldface) :
   3-fold quotients : {2,62}*248
   6-fold quotients : {2,31}*124
   31-fold quotients : {6,2}*24
   62-fold quotients : {3,2}*12
   93-fold quotients : {2,2}*8
Covers (Minimal Covers in Boldface) :
   2-fold covers : {12,62}*1488, {6,124}*1488a
Permutation Representation (GAP) :

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