Polytope of Type {2,62,6}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,62,6}*1488
if this polytope has a name.
Group : SmallGroup(1488,213)
Rank : 4
Schlafli Type : {2,62,6}
Number of vertices, edges, etc : 2, 62, 186, 6
Order of s₀s₁s₂s₃ : 186
Order of s₀s₁s₂s₃s₂s₁ : 2
Special Properties :
   Degenerate
   Universal
   Orientable
   Flat
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   None in this Atlas
Vertex Figure Of :
   None in this Atlas
Quotients (Maximal Quotients in Boldface) :
   3-fold quotients : {2,62,2}*496
   6-fold quotients : {2,31,2}*248
   31-fold quotients : {2,2,6}*48
   62-fold quotients : {2,2,3}*24
   93-fold quotients : {2,2,2}*16
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :

s0 := (1,2);;
s1 := (  4, 33)(  5, 32)(  6, 31)(  7, 30)(  8, 29)(  9, 28)( 10, 27)( 11, 26)
( 12, 25)( 13, 24)( 14, 23)( 15, 22)( 16, 21)( 17, 20)( 18, 19)( 35, 64)
( 36, 63)( 37, 62)( 38, 61)( 39, 60)( 40, 59)( 41, 58)( 42, 57)( 43, 56)
( 44, 55)( 45, 54)( 46, 53)( 47, 52)( 48, 51)( 49, 50)( 66, 95)( 67, 94)
( 68, 93)( 69, 92)( 70, 91)( 71, 90)( 72, 89)( 73, 88)( 74, 87)( 75, 86)
( 76, 85)( 77, 84)( 78, 83)( 79, 82)( 80, 81)( 97,126)( 98,125)( 99,124)
(100,123)(101,122)(102,121)(103,120)(104,119)(105,118)(106,117)(107,116)
(108,115)(109,114)(110,113)(111,112)(128,157)(129,156)(130,155)(131,154)
(132,153)(133,152)(134,151)(135,150)(136,149)(137,148)(138,147)(139,146)
(140,145)(141,144)(142,143)(159,188)(160,187)(161,186)(162,185)(163,184)
(164,183)(165,182)(166,181)(167,180)(168,179)(169,178)(170,177)(171,176)
(172,175)(173,174);;
s2 := (  3,  4)(  5, 33)(  6, 32)(  7, 31)(  8, 30)(  9, 29)( 10, 28)( 11, 27)
( 12, 26)( 13, 25)( 14, 24)( 15, 23)( 16, 22)( 17, 21)( 18, 20)( 34, 66)
( 35, 65)( 36, 95)( 37, 94)( 38, 93)( 39, 92)( 40, 91)( 41, 90)( 42, 89)
( 43, 88)( 44, 87)( 45, 86)( 46, 85)( 47, 84)( 48, 83)( 49, 82)( 50, 81)
( 51, 80)( 52, 79)( 53, 78)( 54, 77)( 55, 76)( 56, 75)( 57, 74)( 58, 73)
( 59, 72)( 60, 71)( 61, 70)( 62, 69)( 63, 68)( 64, 67)( 96, 97)( 98,126)
( 99,125)(100,124)(101,123)(102,122)(103,121)(104,120)(105,119)(106,118)
(107,117)(108,116)(109,115)(110,114)(111,113)(127,159)(128,158)(129,188)
(130,187)(131,186)(132,185)(133,184)(134,183)(135,182)(136,181)(137,180)
(138,179)(139,178)(140,177)(141,176)(142,175)(143,174)(144,173)(145,172)
(146,171)(147,170)(148,169)(149,168)(150,167)(151,166)(152,165)(153,164)
(154,163)(155,162)(156,161)(157,160);;
s3 := (  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)( 32,156)( 33,157)( 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)( 63,125)( 64,126)( 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)( 94,187)( 95,188);;
poly := Group([s0,s1,s2,s3]);;

Finitely Presented Group Representation (GAP) :

F := FreeGroup("s0","s1","s2","s3");;
s0 := F.1;;  s1 := F.2;;  s2 := F.3;;  s3 := F.4;;  
rels := [ s0*s0, s1*s1, s2*s2, s3*s3, s0*s1*s0*s1, 
s0*s2*s0*s2, s0*s3*s0*s3, s1*s3*s1*s3, 
s1*s2*s3*s2*s1*s2*s3*s2, s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3, 
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*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(188)!(1,2);
s1 := Sym(188)!(  4, 33)(  5, 32)(  6, 31)(  7, 30)(  8, 29)(  9, 28)( 10, 27)
( 11, 26)( 12, 25)( 13, 24)( 14, 23)( 15, 22)( 16, 21)( 17, 20)( 18, 19)
( 35, 64)( 36, 63)( 37, 62)( 38, 61)( 39, 60)( 40, 59)( 41, 58)( 42, 57)
( 43, 56)( 44, 55)( 45, 54)( 46, 53)( 47, 52)( 48, 51)( 49, 50)( 66, 95)
( 67, 94)( 68, 93)( 69, 92)( 70, 91)( 71, 90)( 72, 89)( 73, 88)( 74, 87)
( 75, 86)( 76, 85)( 77, 84)( 78, 83)( 79, 82)( 80, 81)( 97,126)( 98,125)
( 99,124)(100,123)(101,122)(102,121)(103,120)(104,119)(105,118)(106,117)
(107,116)(108,115)(109,114)(110,113)(111,112)(128,157)(129,156)(130,155)
(131,154)(132,153)(133,152)(134,151)(135,150)(136,149)(137,148)(138,147)
(139,146)(140,145)(141,144)(142,143)(159,188)(160,187)(161,186)(162,185)
(163,184)(164,183)(165,182)(166,181)(167,180)(168,179)(169,178)(170,177)
(171,176)(172,175)(173,174);
s2 := Sym(188)!(  3,  4)(  5, 33)(  6, 32)(  7, 31)(  8, 30)(  9, 29)( 10, 28)
( 11, 27)( 12, 26)( 13, 25)( 14, 24)( 15, 23)( 16, 22)( 17, 21)( 18, 20)
( 34, 66)( 35, 65)( 36, 95)( 37, 94)( 38, 93)( 39, 92)( 40, 91)( 41, 90)
( 42, 89)( 43, 88)( 44, 87)( 45, 86)( 46, 85)( 47, 84)( 48, 83)( 49, 82)
( 50, 81)( 51, 80)( 52, 79)( 53, 78)( 54, 77)( 55, 76)( 56, 75)( 57, 74)
( 58, 73)( 59, 72)( 60, 71)( 61, 70)( 62, 69)( 63, 68)( 64, 67)( 96, 97)
( 98,126)( 99,125)(100,124)(101,123)(102,122)(103,121)(104,120)(105,119)
(106,118)(107,117)(108,116)(109,115)(110,114)(111,113)(127,159)(128,158)
(129,188)(130,187)(131,186)(132,185)(133,184)(134,183)(135,182)(136,181)
(137,180)(138,179)(139,178)(140,177)(141,176)(142,175)(143,174)(144,173)
(145,172)(146,171)(147,170)(148,169)(149,168)(150,167)(151,166)(152,165)
(153,164)(154,163)(155,162)(156,161)(157,160);
s3 := Sym(188)!(  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)( 32,156)( 33,157)
( 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)( 63,125)( 64,126)( 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)( 94,187)( 95,188);
poly := sub<Sym(188)|s0,s1,s2,s3>;

Finitely Presented Group Representation (Magma) :

poly<s0,s1,s2,s3> := Group< s0,s1,s2,s3 | s0*s0, s1*s1, s2*s2, 
s3*s3, s0*s1*s0*s1, s0*s2*s0*s2, s0*s3*s0*s3, 
s1*s3*s1*s3, s1*s2*s3*s2*s1*s2*s3*s2, 
s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3, 
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2 >;

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