Polytope of Type {4,6,34}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {4,6,34}*1632a
Also Known As : {{4,6|2},{6,34|2}}. if this polytope has another name.
Group : SmallGroup(1632,1097)
Rank : 4
Schlafli Type : {4,6,34}
Number of vertices, edges, etc : 4, 12, 102, 34
Order of s₀s₁s₂s₃ : 204
Order of s₀s₁s₂s₃s₂s₁ : 2
Special Properties :
   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 : {2,6,34}*816
   3-fold quotients : {4,2,34}*544
   6-fold quotients : {4,2,17}*272, {2,2,34}*272
   12-fold quotients : {2,2,17}*136
   17-fold quotients : {4,6,2}*96a
   34-fold quotients : {2,6,2}*48
   51-fold quotients : {4,2,2}*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 := (103,154)(104,155)(105,156)(106,157)(107,158)(108,159)(109,160)(110,161)
(111,162)(112,163)(113,164)(114,165)(115,166)(116,167)(117,168)(118,169)
(119,170)(120,171)(121,172)(122,173)(123,174)(124,175)(125,176)(126,177)
(127,178)(128,179)(129,180)(130,181)(131,182)(132,183)(133,184)(134,185)
(135,186)(136,187)(137,188)(138,189)(139,190)(140,191)(141,192)(142,193)
(143,194)(144,195)(145,196)(146,197)(147,198)(148,199)(149,200)(150,201)
(151,202)(152,203)(153,204);;
s1 := (  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)( 18,137)( 19,138)( 20,139)( 21,140)( 22,141)( 23,142)( 24,143)
( 25,144)( 26,145)( 27,146)( 28,147)( 29,148)( 30,149)( 31,150)( 32,151)
( 33,152)( 34,153)( 35,120)( 36,121)( 37,122)( 38,123)( 39,124)( 40,125)
( 41,126)( 42,127)( 43,128)( 44,129)( 45,130)( 46,131)( 47,132)( 48,133)
( 49,134)( 50,135)( 51,136)( 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)( 69,188)( 70,189)( 71,190)( 72,191)
( 73,192)( 74,193)( 75,194)( 76,195)( 77,196)( 78,197)( 79,198)( 80,199)
( 81,200)( 82,201)( 83,202)( 84,203)( 85,204)( 86,171)( 87,172)( 88,173)
( 89,174)( 90,175)( 91,176)( 92,177)( 93,178)( 94,179)( 95,180)( 96,181)
( 97,182)( 98,183)( 99,184)(100,185)(101,186)(102,187);;
s2 := (  1, 18)(  2, 34)(  3, 33)(  4, 32)(  5, 31)(  6, 30)(  7, 29)(  8, 28)
(  9, 27)( 10, 26)( 11, 25)( 12, 24)( 13, 23)( 14, 22)( 15, 21)( 16, 20)
( 17, 19)( 36, 51)( 37, 50)( 38, 49)( 39, 48)( 40, 47)( 41, 46)( 42, 45)
( 43, 44)( 52, 69)( 53, 85)( 54, 84)( 55, 83)( 56, 82)( 57, 81)( 58, 80)
( 59, 79)( 60, 78)( 61, 77)( 62, 76)( 63, 75)( 64, 74)( 65, 73)( 66, 72)
( 67, 71)( 68, 70)( 87,102)( 88,101)( 89,100)( 90, 99)( 91, 98)( 92, 97)
( 93, 96)( 94, 95)(103,120)(104,136)(105,135)(106,134)(107,133)(108,132)
(109,131)(110,130)(111,129)(112,128)(113,127)(114,126)(115,125)(116,124)
(117,123)(118,122)(119,121)(138,153)(139,152)(140,151)(141,150)(142,149)
(143,148)(144,147)(145,146)(154,171)(155,187)(156,186)(157,185)(158,184)
(159,183)(160,182)(161,181)(162,180)(163,179)(164,178)(165,177)(166,176)
(167,175)(168,174)(169,173)(170,172)(189,204)(190,203)(191,202)(192,201)
(193,200)(194,199)(195,198)(196,197);;
s3 := (  1,  2)(  3, 17)(  4, 16)(  5, 15)(  6, 14)(  7, 13)(  8, 12)(  9, 11)
( 18, 19)( 20, 34)( 21, 33)( 22, 32)( 23, 31)( 24, 30)( 25, 29)( 26, 28)
( 35, 36)( 37, 51)( 38, 50)( 39, 49)( 40, 48)( 41, 47)( 42, 46)( 43, 45)
( 52, 53)( 54, 68)( 55, 67)( 56, 66)( 57, 65)( 58, 64)( 59, 63)( 60, 62)
( 69, 70)( 71, 85)( 72, 84)( 73, 83)( 74, 82)( 75, 81)( 76, 80)( 77, 79)
( 86, 87)( 88,102)( 89,101)( 90,100)( 91, 99)( 92, 98)( 93, 97)( 94, 96)
(103,104)(105,119)(106,118)(107,117)(108,116)(109,115)(110,114)(111,113)
(120,121)(122,136)(123,135)(124,134)(125,133)(126,132)(127,131)(128,130)
(137,138)(139,153)(140,152)(141,151)(142,150)(143,149)(144,148)(145,147)
(154,155)(156,170)(157,169)(158,168)(159,167)(160,166)(161,165)(162,164)
(171,172)(173,187)(174,186)(175,185)(176,184)(177,183)(178,182)(179,181)
(188,189)(190,204)(191,203)(192,202)(193,201)(194,200)(195,199)(196,198);;
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*s2*s0*s2, 
s0*s3*s0*s3, s1*s3*s1*s3, s0*s1*s0*s1*s0*s1*s0*s1, 
s0*s1*s2*s1*s0*s1*s2*s1, s1*s2*s3*s2*s1*s2*s3*s2, 
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*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*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3 ];;
poly := F / rels;;

Permutation Representation (Magma) :

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

References : None.
to this polytope