Polytope of Type {2,12,34}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,12,34}*1632
if this polytope has a name.
Group : SmallGroup(1632,1087)
Rank : 4
Schlafli Type : {2,12,34}
Number of vertices, edges, etc : 2, 12, 204, 34
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 : {2,6,34}*816
   3-fold quotients : {2,4,34}*544
   6-fold quotients : {2,2,34}*272
   12-fold quotients : {2,2,17}*136
   17-fold quotients : {2,12,2}*96
   34-fold quotients : {2,6,2}*48
   51-fold quotients : {2,4,2}*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 := (1,2);;
s1 := ( 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)( 35, 52)
( 36, 53)( 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)
( 86,103)( 87,104)(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)(122,190)(123,191)(124,192)(125,193)(126,194)
(127,195)(128,196)(129,197)(130,198)(131,199)(132,200)(133,201)(134,202)
(135,203)(136,204)(137,205)(138,206)(139,173)(140,174)(141,175)(142,176)
(143,177)(144,178)(145,179)(146,180)(147,181)(148,182)(149,183)(150,184)
(151,185)(152,186)(153,187)(154,188)(155,189);;
s2 := (  3,122)(  4,138)(  5,137)(  6,136)(  7,135)(  8,134)(  9,133)( 10,132)
( 11,131)( 12,130)( 13,129)( 14,128)( 15,127)( 16,126)( 17,125)( 18,124)
( 19,123)( 20,105)( 21,121)( 22,120)( 23,119)( 24,118)( 25,117)( 26,116)
( 27,115)( 28,114)( 29,113)( 30,112)( 31,111)( 32,110)( 33,109)( 34,108)
( 35,107)( 36,106)( 37,139)( 38,155)( 39,154)( 40,153)( 41,152)( 42,151)
( 43,150)( 44,149)( 45,148)( 46,147)( 47,146)( 48,145)( 49,144)( 50,143)
( 51,142)( 52,141)( 53,140)( 54,173)( 55,189)( 56,188)( 57,187)( 58,186)
( 59,185)( 60,184)( 61,183)( 62,182)( 63,181)( 64,180)( 65,179)( 66,178)
( 67,177)( 68,176)( 69,175)( 70,174)( 71,156)( 72,172)( 73,171)( 74,170)
( 75,169)( 76,168)( 77,167)( 78,166)( 79,165)( 80,164)( 81,163)( 82,162)
( 83,161)( 84,160)( 85,159)( 86,158)( 87,157)( 88,190)( 89,206)( 90,205)
( 91,204)( 92,203)( 93,202)( 94,201)( 95,200)( 96,199)( 97,198)( 98,197)
( 99,196)(100,195)(101,194)(102,193)(103,192)(104,191);;
s3 := (  3,  4)(  5, 19)(  6, 18)(  7, 17)(  8, 16)(  9, 15)( 10, 14)( 11, 13)
( 20, 21)( 22, 36)( 23, 35)( 24, 34)( 25, 33)( 26, 32)( 27, 31)( 28, 30)
( 37, 38)( 39, 53)( 40, 52)( 41, 51)( 42, 50)( 43, 49)( 44, 48)( 45, 47)
( 54, 55)( 56, 70)( 57, 69)( 58, 68)( 59, 67)( 60, 66)( 61, 65)( 62, 64)
( 71, 72)( 73, 87)( 74, 86)( 75, 85)( 76, 84)( 77, 83)( 78, 82)( 79, 81)
( 88, 89)( 90,104)( 91,103)( 92,102)( 93,101)( 94,100)( 95, 99)( 96, 98)
(105,106)(107,121)(108,120)(109,119)(110,118)(111,117)(112,116)(113,115)
(122,123)(124,138)(125,137)(126,136)(127,135)(128,134)(129,133)(130,132)
(139,140)(141,155)(142,154)(143,153)(144,152)(145,151)(146,150)(147,149)
(156,157)(158,172)(159,171)(160,170)(161,169)(162,168)(163,167)(164,166)
(173,174)(175,189)(176,188)(177,187)(178,186)(179,185)(180,184)(181,183)
(190,191)(192,206)(193,205)(194,204)(195,203)(196,202)(197,201)(198,200);;
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, s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*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(206)!(1,2);
s1 := Sym(206)!( 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)
( 35, 52)( 36, 53)( 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)( 86,103)( 87,104)(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)(122,190)(123,191)(124,192)(125,193)
(126,194)(127,195)(128,196)(129,197)(130,198)(131,199)(132,200)(133,201)
(134,202)(135,203)(136,204)(137,205)(138,206)(139,173)(140,174)(141,175)
(142,176)(143,177)(144,178)(145,179)(146,180)(147,181)(148,182)(149,183)
(150,184)(151,185)(152,186)(153,187)(154,188)(155,189);
s2 := Sym(206)!(  3,122)(  4,138)(  5,137)(  6,136)(  7,135)(  8,134)(  9,133)
( 10,132)( 11,131)( 12,130)( 13,129)( 14,128)( 15,127)( 16,126)( 17,125)
( 18,124)( 19,123)( 20,105)( 21,121)( 22,120)( 23,119)( 24,118)( 25,117)
( 26,116)( 27,115)( 28,114)( 29,113)( 30,112)( 31,111)( 32,110)( 33,109)
( 34,108)( 35,107)( 36,106)( 37,139)( 38,155)( 39,154)( 40,153)( 41,152)
( 42,151)( 43,150)( 44,149)( 45,148)( 46,147)( 47,146)( 48,145)( 49,144)
( 50,143)( 51,142)( 52,141)( 53,140)( 54,173)( 55,189)( 56,188)( 57,187)
( 58,186)( 59,185)( 60,184)( 61,183)( 62,182)( 63,181)( 64,180)( 65,179)
( 66,178)( 67,177)( 68,176)( 69,175)( 70,174)( 71,156)( 72,172)( 73,171)
( 74,170)( 75,169)( 76,168)( 77,167)( 78,166)( 79,165)( 80,164)( 81,163)
( 82,162)( 83,161)( 84,160)( 85,159)( 86,158)( 87,157)( 88,190)( 89,206)
( 90,205)( 91,204)( 92,203)( 93,202)( 94,201)( 95,200)( 96,199)( 97,198)
( 98,197)( 99,196)(100,195)(101,194)(102,193)(103,192)(104,191);
s3 := Sym(206)!(  3,  4)(  5, 19)(  6, 18)(  7, 17)(  8, 16)(  9, 15)( 10, 14)
( 11, 13)( 20, 21)( 22, 36)( 23, 35)( 24, 34)( 25, 33)( 26, 32)( 27, 31)
( 28, 30)( 37, 38)( 39, 53)( 40, 52)( 41, 51)( 42, 50)( 43, 49)( 44, 48)
( 45, 47)( 54, 55)( 56, 70)( 57, 69)( 58, 68)( 59, 67)( 60, 66)( 61, 65)
( 62, 64)( 71, 72)( 73, 87)( 74, 86)( 75, 85)( 76, 84)( 77, 83)( 78, 82)
( 79, 81)( 88, 89)( 90,104)( 91,103)( 92,102)( 93,101)( 94,100)( 95, 99)
( 96, 98)(105,106)(107,121)(108,120)(109,119)(110,118)(111,117)(112,116)
(113,115)(122,123)(124,138)(125,137)(126,136)(127,135)(128,134)(129,133)
(130,132)(139,140)(141,155)(142,154)(143,153)(144,152)(145,151)(146,150)
(147,149)(156,157)(158,172)(159,171)(160,170)(161,169)(162,168)(163,167)
(164,166)(173,174)(175,189)(176,188)(177,187)(178,186)(179,185)(180,184)
(181,183)(190,191)(192,206)(193,205)(194,204)(195,203)(196,202)(197,201)
(198,200);
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, 
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*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 >;

to this polytope