Polytope of Type {6,34,4}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {6,34,4}*1632
Also Known As : {{6,34|2},{34,4|2}}. if this polytope has another name.
Group : SmallGroup(1632,1097)
Rank : 4
Schlafli Type : {6,34,4}
Number of vertices, edges, etc : 6, 102, 68, 4
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 : {6,34,2}*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 : {6,2,4}*96
   34-fold quotients : {3,2,4}*48, {6,2,2}*48
   51-fold quotients : {2,2,4}*32
   68-fold quotients : {3,2,2}*24
   102-fold quotients : {2,2,2}*16
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :

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

References : None.
to this polytope