Polytope of Type {102,4}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {102,4}*816a
Also Known As : {102,4|2}. if this polytope has another name.
Group : SmallGroup(816,175)
Rank : 3
Schlafli Type : {102,4}
Number of vertices, edges, etc : 102, 204, 4
Order of s₀s₁s₂ : 204
Order of s₀s₁s₂s₁ : 2
Special Properties :
   Compact Hyperbolic Quotient
   Locally Spherical
   Orientable
   Flat
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   {102,4,2} of size 1632
Vertex Figure Of :
   {2,102,4} of size 1632
Quotients (Maximal Quotients in Boldface) :
   2-fold quotients : {102,2}*408
   3-fold quotients : {34,4}*272
   4-fold quotients : {51,2}*204
   6-fold quotients : {34,2}*136
   12-fold quotients : {17,2}*68
   17-fold quotients : {6,4}*48a
   34-fold quotients : {6,2}*24
   51-fold quotients : {2,4}*16
   68-fold quotients : {3,2}*12
   102-fold quotients : {2,2}*8
Covers (Minimal Covers in Boldface) :
   2-fold covers : {204,4}*1632a, {102,8}*1632
Permutation Representation (GAP) :

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