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Polytope of Type {2,34,12}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,34,12}*1632
if this polytope has a name.
Group : SmallGroup(1632,1087)
Rank : 4
Schlafli Type : {2,34,12}
Number of vertices, edges, etc : 2, 34, 204, 12
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 : {2,34,6}*816
   3-fold quotients : {2,34,4}*544
   6-fold quotients : {2,34,2}*272
   12-fold quotients : {2,17,2}*136
   17-fold quotients : {2,2,12}*96
   34-fold quotients : {2,2,6}*48
   51-fold quotients : {2,2,4}*32
   68-fold quotients : {2,2,3}*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)
( 21, 36)( 22, 35)( 23, 34)( 24, 33)( 25, 32)( 26, 31)( 27, 30)( 28, 29)
( 38, 53)( 39, 52)( 40, 51)( 41, 50)( 42, 49)( 43, 48)( 44, 47)( 45, 46)
( 55, 70)( 56, 69)( 57, 68)( 58, 67)( 59, 66)( 60, 65)( 61, 64)( 62, 63)
( 72, 87)( 73, 86)( 74, 85)( 75, 84)( 76, 83)( 77, 82)( 78, 81)( 79, 80)
( 89,104)( 90,103)( 91,102)( 92,101)( 93,100)( 94, 99)( 95, 98)( 96, 97)
(106,121)(107,120)(108,119)(109,118)(110,117)(111,116)(112,115)(113,114)
(123,138)(124,137)(125,136)(126,135)(127,134)(128,133)(129,132)(130,131)
(140,155)(141,154)(142,153)(143,152)(144,151)(145,150)(146,149)(147,148)
(157,172)(158,171)(159,170)(160,169)(161,168)(162,167)(163,166)(164,165)
(174,189)(175,188)(176,187)(177,186)(178,185)(179,184)(180,183)(181,182)
(191,206)(192,205)(193,204)(194,203)(195,202)(196,201)(197,200)(198,199);;
s2 := (  3,  4)(  5, 19)(  6, 18)(  7, 17)(  8, 16)(  9, 15)( 10, 14)( 11, 13)
( 20, 38)( 21, 37)( 22, 53)( 23, 52)( 24, 51)( 25, 50)( 26, 49)( 27, 48)
( 28, 47)( 29, 46)( 30, 45)( 31, 44)( 32, 43)( 33, 42)( 34, 41)( 35, 40)
( 36, 39)( 54, 55)( 56, 70)( 57, 69)( 58, 68)( 59, 67)( 60, 66)( 61, 65)
( 62, 64)( 71, 89)( 72, 88)( 73,104)( 74,103)( 75,102)( 76,101)( 77,100)
( 78, 99)( 79, 98)( 80, 97)( 81, 96)( 82, 95)( 83, 94)( 84, 93)( 85, 92)
( 86, 91)( 87, 90)(105,157)(106,156)(107,172)(108,171)(109,170)(110,169)
(111,168)(112,167)(113,166)(114,165)(115,164)(116,163)(117,162)(118,161)
(119,160)(120,159)(121,158)(122,191)(123,190)(124,206)(125,205)(126,204)
(127,203)(128,202)(129,201)(130,200)(131,199)(132,198)(133,197)(134,196)
(135,195)(136,194)(137,193)(138,192)(139,174)(140,173)(141,189)(142,188)
(143,187)(144,186)(145,185)(146,184)(147,183)(148,182)(149,181)(150,180)
(151,179)(152,178)(153,177)(154,176)(155,175);;
s3 := (  3,122)(  4,123)(  5,124)(  6,125)(  7,126)(  8,127)(  9,128)( 10,129)
( 11,130)( 12,131)( 13,132)( 14,133)( 15,134)( 16,135)( 17,136)( 18,137)
( 19,138)( 20,105)( 21,106)( 22,107)( 23,108)( 24,109)( 25,110)( 26,111)
( 27,112)( 28,113)( 29,114)( 30,115)( 31,116)( 32,117)( 33,118)( 34,119)
( 35,120)( 36,121)( 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)( 54,173)( 55,174)( 56,175)( 57,176)( 58,177)
( 59,178)( 60,179)( 61,180)( 62,181)( 63,182)( 64,183)( 65,184)( 66,185)
( 67,186)( 68,187)( 69,188)( 70,189)( 71,156)( 72,157)( 73,158)( 74,159)
( 75,160)( 76,161)( 77,162)( 78,163)( 79,164)( 80,165)( 81,166)( 82,167)
( 83,168)( 84,169)( 85,170)( 86,171)( 87,172)( 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*s2*s3*s2*s3*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 ];;
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)( 21, 36)( 22, 35)( 23, 34)( 24, 33)( 25, 32)( 26, 31)( 27, 30)
( 28, 29)( 38, 53)( 39, 52)( 40, 51)( 41, 50)( 42, 49)( 43, 48)( 44, 47)
( 45, 46)( 55, 70)( 56, 69)( 57, 68)( 58, 67)( 59, 66)( 60, 65)( 61, 64)
( 62, 63)( 72, 87)( 73, 86)( 74, 85)( 75, 84)( 76, 83)( 77, 82)( 78, 81)
( 79, 80)( 89,104)( 90,103)( 91,102)( 92,101)( 93,100)( 94, 99)( 95, 98)
( 96, 97)(106,121)(107,120)(108,119)(109,118)(110,117)(111,116)(112,115)
(113,114)(123,138)(124,137)(125,136)(126,135)(127,134)(128,133)(129,132)
(130,131)(140,155)(141,154)(142,153)(143,152)(144,151)(145,150)(146,149)
(147,148)(157,172)(158,171)(159,170)(160,169)(161,168)(162,167)(163,166)
(164,165)(174,189)(175,188)(176,187)(177,186)(178,185)(179,184)(180,183)
(181,182)(191,206)(192,205)(193,204)(194,203)(195,202)(196,201)(197,200)
(198,199);
s2 := Sym(206)!(  3,  4)(  5, 19)(  6, 18)(  7, 17)(  8, 16)(  9, 15)( 10, 14)
( 11, 13)( 20, 38)( 21, 37)( 22, 53)( 23, 52)( 24, 51)( 25, 50)( 26, 49)
( 27, 48)( 28, 47)( 29, 46)( 30, 45)( 31, 44)( 32, 43)( 33, 42)( 34, 41)
( 35, 40)( 36, 39)( 54, 55)( 56, 70)( 57, 69)( 58, 68)( 59, 67)( 60, 66)
( 61, 65)( 62, 64)( 71, 89)( 72, 88)( 73,104)( 74,103)( 75,102)( 76,101)
( 77,100)( 78, 99)( 79, 98)( 80, 97)( 81, 96)( 82, 95)( 83, 94)( 84, 93)
( 85, 92)( 86, 91)( 87, 90)(105,157)(106,156)(107,172)(108,171)(109,170)
(110,169)(111,168)(112,167)(113,166)(114,165)(115,164)(116,163)(117,162)
(118,161)(119,160)(120,159)(121,158)(122,191)(123,190)(124,206)(125,205)
(126,204)(127,203)(128,202)(129,201)(130,200)(131,199)(132,198)(133,197)
(134,196)(135,195)(136,194)(137,193)(138,192)(139,174)(140,173)(141,189)
(142,188)(143,187)(144,186)(145,185)(146,184)(147,183)(148,182)(149,181)
(150,180)(151,179)(152,178)(153,177)(154,176)(155,175);
s3 := Sym(206)!(  3,122)(  4,123)(  5,124)(  6,125)(  7,126)(  8,127)(  9,128)
( 10,129)( 11,130)( 12,131)( 13,132)( 14,133)( 15,134)( 16,135)( 17,136)
( 18,137)( 19,138)( 20,105)( 21,106)( 22,107)( 23,108)( 24,109)( 25,110)
( 26,111)( 27,112)( 28,113)( 29,114)( 30,115)( 31,116)( 32,117)( 33,118)
( 34,119)( 35,120)( 36,121)( 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)( 54,173)( 55,174)( 56,175)( 57,176)
( 58,177)( 59,178)( 60,179)( 61,180)( 62,181)( 63,182)( 64,183)( 65,184)
( 66,185)( 67,186)( 68,187)( 69,188)( 70,189)( 71,156)( 72,157)( 73,158)
( 74,159)( 75,160)( 76,161)( 77,162)( 78,163)( 79,164)( 80,165)( 81,166)
( 82,167)( 83,168)( 84,169)( 85,170)( 86,171)( 87,172)( 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*s2*s3*s2*s3*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 >; 
 

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