Polytope of Type {2,102,4}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,102,4}*1632a
if this polytope has a name.
Group : SmallGroup(1632,1169)
Rank : 4
Schlafli Type : {2,102,4}
Number of vertices, edges, etc : 2, 102, 204, 4
Order of s₀s₁s₂s₃ : 204
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) :
   2-fold quotients : {2,102,2}*816
   3-fold quotients : {2,34,4}*544
   4-fold quotients : {2,51,2}*408
   6-fold quotients : {2,34,2}*272
   12-fold quotients : {2,17,2}*136
   17-fold quotients : {2,6,4}*96a
   34-fold quotients : {2,6,2}*48
   51-fold quotients : {2,2,4}*32
   68-fold quotients : {2,3,2}*24
   102-fold quotients : {2,2,2}*16
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :

s0 := (1,2);;
s1 := (  4, 19)(  5, 18)(  6, 17)(  7, 16)(  8, 15)(  9, 14)( 10, 13)( 11, 12)
( 20, 37)( 21, 53)( 22, 52)( 23, 51)( 24, 50)( 25, 49)( 26, 48)( 27, 47)
( 28, 46)( 29, 45)( 30, 44)( 31, 43)( 32, 42)( 33, 41)( 34, 40)( 35, 39)
( 36, 38)( 55, 70)( 56, 69)( 57, 68)( 58, 67)( 59, 66)( 60, 65)( 61, 64)
( 62, 63)( 71, 88)( 72,104)( 73,103)( 74,102)( 75,101)( 76,100)( 77, 99)
( 78, 98)( 79, 97)( 80, 96)( 81, 95)( 82, 94)( 83, 93)( 84, 92)( 85, 91)
( 86, 90)( 87, 89)(106,121)(107,120)(108,119)(109,118)(110,117)(111,116)
(112,115)(113,114)(122,139)(123,155)(124,154)(125,153)(126,152)(127,151)
(128,150)(129,149)(130,148)(131,147)(132,146)(133,145)(134,144)(135,143)
(136,142)(137,141)(138,140)(157,172)(158,171)(159,170)(160,169)(161,168)
(162,167)(163,166)(164,165)(173,190)(174,206)(175,205)(176,204)(177,203)
(178,202)(179,201)(180,200)(181,199)(182,198)(183,197)(184,196)(185,195)
(186,194)(187,193)(188,192)(189,191);;
s2 := (  3, 21)(  4, 20)(  5, 36)(  6, 35)(  7, 34)(  8, 33)(  9, 32)( 10, 31)
( 11, 30)( 12, 29)( 13, 28)( 14, 27)( 15, 26)( 16, 25)( 17, 24)( 18, 23)
( 19, 22)( 37, 38)( 39, 53)( 40, 52)( 41, 51)( 42, 50)( 43, 49)( 44, 48)
( 45, 47)( 54, 72)( 55, 71)( 56, 87)( 57, 86)( 58, 85)( 59, 84)( 60, 83)
( 61, 82)( 62, 81)( 63, 80)( 64, 79)( 65, 78)( 66, 77)( 67, 76)( 68, 75)
( 69, 74)( 70, 73)( 88, 89)( 90,104)( 91,103)( 92,102)( 93,101)( 94,100)
( 95, 99)( 96, 98)(105,174)(106,173)(107,189)(108,188)(109,187)(110,186)
(111,185)(112,184)(113,183)(114,182)(115,181)(116,180)(117,179)(118,178)
(119,177)(120,176)(121,175)(122,157)(123,156)(124,172)(125,171)(126,170)
(127,169)(128,168)(129,167)(130,166)(131,165)(132,164)(133,163)(134,162)
(135,161)(136,160)(137,159)(138,158)(139,191)(140,190)(141,206)(142,205)
(143,204)(144,203)(145,202)(146,201)(147,200)(148,199)(149,198)(150,197)
(151,196)(152,195)(153,194)(154,193)(155,192);;
s3 := (  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)(103,205)(104,206);;
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, 
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*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(206)!(1,2);
s1 := Sym(206)!(  4, 19)(  5, 18)(  6, 17)(  7, 16)(  8, 15)(  9, 14)( 10, 13)
( 11, 12)( 20, 37)( 21, 53)( 22, 52)( 23, 51)( 24, 50)( 25, 49)( 26, 48)
( 27, 47)( 28, 46)( 29, 45)( 30, 44)( 31, 43)( 32, 42)( 33, 41)( 34, 40)
( 35, 39)( 36, 38)( 55, 70)( 56, 69)( 57, 68)( 58, 67)( 59, 66)( 60, 65)
( 61, 64)( 62, 63)( 71, 88)( 72,104)( 73,103)( 74,102)( 75,101)( 76,100)
( 77, 99)( 78, 98)( 79, 97)( 80, 96)( 81, 95)( 82, 94)( 83, 93)( 84, 92)
( 85, 91)( 86, 90)( 87, 89)(106,121)(107,120)(108,119)(109,118)(110,117)
(111,116)(112,115)(113,114)(122,139)(123,155)(124,154)(125,153)(126,152)
(127,151)(128,150)(129,149)(130,148)(131,147)(132,146)(133,145)(134,144)
(135,143)(136,142)(137,141)(138,140)(157,172)(158,171)(159,170)(160,169)
(161,168)(162,167)(163,166)(164,165)(173,190)(174,206)(175,205)(176,204)
(177,203)(178,202)(179,201)(180,200)(181,199)(182,198)(183,197)(184,196)
(185,195)(186,194)(187,193)(188,192)(189,191);
s2 := Sym(206)!(  3, 21)(  4, 20)(  5, 36)(  6, 35)(  7, 34)(  8, 33)(  9, 32)
( 10, 31)( 11, 30)( 12, 29)( 13, 28)( 14, 27)( 15, 26)( 16, 25)( 17, 24)
( 18, 23)( 19, 22)( 37, 38)( 39, 53)( 40, 52)( 41, 51)( 42, 50)( 43, 49)
( 44, 48)( 45, 47)( 54, 72)( 55, 71)( 56, 87)( 57, 86)( 58, 85)( 59, 84)
( 60, 83)( 61, 82)( 62, 81)( 63, 80)( 64, 79)( 65, 78)( 66, 77)( 67, 76)
( 68, 75)( 69, 74)( 70, 73)( 88, 89)( 90,104)( 91,103)( 92,102)( 93,101)
( 94,100)( 95, 99)( 96, 98)(105,174)(106,173)(107,189)(108,188)(109,187)
(110,186)(111,185)(112,184)(113,183)(114,182)(115,181)(116,180)(117,179)
(118,178)(119,177)(120,176)(121,175)(122,157)(123,156)(124,172)(125,171)
(126,170)(127,169)(128,168)(129,167)(130,166)(131,165)(132,164)(133,163)
(134,162)(135,161)(136,160)(137,159)(138,158)(139,191)(140,190)(141,206)
(142,205)(143,204)(144,203)(145,202)(146,201)(147,200)(148,199)(149,198)
(150,197)(151,196)(152,195)(153,194)(154,193)(155,192);
s3 := Sym(206)!(  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)(103,205)(104,206);
poly := sub<Sym(206)|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, s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2 >;

to this polytope