Polytope of Type {62,6}

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

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

Permutation Representation (Magma) :

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

References : None.
to this polytope