Polytope of Type {4,102,2}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {4,102,2}*1632a
if this polytope has a name.
Group : SmallGroup(1632,1169)
Rank : 4
Schlafli Type : {4,102,2}
Number of vertices, edges, etc : 4, 204, 102, 2
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 : {4,34,2}*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 : {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)(  2,119)(  3,118)(  4,117)(  5,116)(  6,115)(  7,114)(  8,113)
(  9,112)( 10,111)( 11,110)( 12,109)( 13,108)( 14,107)( 15,106)( 16,105)
( 17,104)( 18,137)( 19,153)( 20,152)( 21,151)( 22,150)( 23,149)( 24,148)
( 25,147)( 26,146)( 27,145)( 28,144)( 29,143)( 30,142)( 31,141)( 32,140)
( 33,139)( 34,138)( 35,120)( 36,136)( 37,135)( 38,134)( 39,133)( 40,132)
( 41,131)( 42,130)( 43,129)( 44,128)( 45,127)( 46,126)( 47,125)( 48,124)
( 49,123)( 50,122)( 51,121)( 52,154)( 53,170)( 54,169)( 55,168)( 56,167)
( 57,166)( 58,165)( 59,164)( 60,163)( 61,162)( 62,161)( 63,160)( 64,159)
( 65,158)( 66,157)( 67,156)( 68,155)( 69,188)( 70,204)( 71,203)( 72,202)
( 73,201)( 74,200)( 75,199)( 76,198)( 77,197)( 78,196)( 79,195)( 80,194)
( 81,193)( 82,192)( 83,191)( 84,190)( 85,189)( 86,171)( 87,187)( 88,186)
( 89,185)( 90,184)( 91,183)( 92,182)( 93,181)( 94,180)( 95,179)( 96,178)
( 97,177)( 98,176)( 99,175)(100,174)(101,173)(102,172);;
s2 := (  1, 19)(  2, 18)(  3, 34)(  4, 33)(  5, 32)(  6, 31)(  7, 30)(  8, 29)
(  9, 28)( 10, 27)( 11, 26)( 12, 25)( 13, 24)( 14, 23)( 15, 22)( 16, 21)
( 17, 20)( 35, 36)( 37, 51)( 38, 50)( 39, 49)( 40, 48)( 41, 47)( 42, 46)
( 43, 45)( 52, 70)( 53, 69)( 54, 85)( 55, 84)( 56, 83)( 57, 82)( 58, 81)
( 59, 80)( 60, 79)( 61, 78)( 62, 77)( 63, 76)( 64, 75)( 65, 74)( 66, 73)
( 67, 72)( 68, 71)( 86, 87)( 88,102)( 89,101)( 90,100)( 91, 99)( 92, 98)
( 93, 97)( 94, 96)(103,121)(104,120)(105,136)(106,135)(107,134)(108,133)
(109,132)(110,131)(111,130)(112,129)(113,128)(114,127)(115,126)(116,125)
(117,124)(118,123)(119,122)(137,138)(139,153)(140,152)(141,151)(142,150)
(143,149)(144,148)(145,147)(154,172)(155,171)(156,187)(157,186)(158,185)
(159,184)(160,183)(161,182)(162,181)(163,180)(164,179)(165,178)(166,177)
(167,176)(168,175)(169,174)(170,173)(188,189)(190,204)(191,203)(192,202)
(193,201)(194,200)(195,199)(196,198);;
s3 := (205,206);;
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*s2*s0*s2, 
s0*s3*s0*s3, s1*s3*s1*s3, s2*s3*s2*s3, 
s0*s1*s0*s1*s0*s1*s0*s1, s0*s1*s2*s1*s0*s1*s2*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*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*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)!(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(206)!(  1,103)(  2,119)(  3,118)(  4,117)(  5,116)(  6,115)(  7,114)
(  8,113)(  9,112)( 10,111)( 11,110)( 12,109)( 13,108)( 14,107)( 15,106)
( 16,105)( 17,104)( 18,137)( 19,153)( 20,152)( 21,151)( 22,150)( 23,149)
( 24,148)( 25,147)( 26,146)( 27,145)( 28,144)( 29,143)( 30,142)( 31,141)
( 32,140)( 33,139)( 34,138)( 35,120)( 36,136)( 37,135)( 38,134)( 39,133)
( 40,132)( 41,131)( 42,130)( 43,129)( 44,128)( 45,127)( 46,126)( 47,125)
( 48,124)( 49,123)( 50,122)( 51,121)( 52,154)( 53,170)( 54,169)( 55,168)
( 56,167)( 57,166)( 58,165)( 59,164)( 60,163)( 61,162)( 62,161)( 63,160)
( 64,159)( 65,158)( 66,157)( 67,156)( 68,155)( 69,188)( 70,204)( 71,203)
( 72,202)( 73,201)( 74,200)( 75,199)( 76,198)( 77,197)( 78,196)( 79,195)
( 80,194)( 81,193)( 82,192)( 83,191)( 84,190)( 85,189)( 86,171)( 87,187)
( 88,186)( 89,185)( 90,184)( 91,183)( 92,182)( 93,181)( 94,180)( 95,179)
( 96,178)( 97,177)( 98,176)( 99,175)(100,174)(101,173)(102,172);
s2 := Sym(206)!(  1, 19)(  2, 18)(  3, 34)(  4, 33)(  5, 32)(  6, 31)(  7, 30)
(  8, 29)(  9, 28)( 10, 27)( 11, 26)( 12, 25)( 13, 24)( 14, 23)( 15, 22)
( 16, 21)( 17, 20)( 35, 36)( 37, 51)( 38, 50)( 39, 49)( 40, 48)( 41, 47)
( 42, 46)( 43, 45)( 52, 70)( 53, 69)( 54, 85)( 55, 84)( 56, 83)( 57, 82)
( 58, 81)( 59, 80)( 60, 79)( 61, 78)( 62, 77)( 63, 76)( 64, 75)( 65, 74)
( 66, 73)( 67, 72)( 68, 71)( 86, 87)( 88,102)( 89,101)( 90,100)( 91, 99)
( 92, 98)( 93, 97)( 94, 96)(103,121)(104,120)(105,136)(106,135)(107,134)
(108,133)(109,132)(110,131)(111,130)(112,129)(113,128)(114,127)(115,126)
(116,125)(117,124)(118,123)(119,122)(137,138)(139,153)(140,152)(141,151)
(142,150)(143,149)(144,148)(145,147)(154,172)(155,171)(156,187)(157,186)
(158,185)(159,184)(160,183)(161,182)(162,181)(163,180)(164,179)(165,178)
(166,177)(167,176)(168,175)(169,174)(170,173)(188,189)(190,204)(191,203)
(192,202)(193,201)(194,200)(195,199)(196,198);
s3 := Sym(206)!(205,206);
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*s2*s0*s2, s0*s3*s0*s3, s1*s3*s1*s3, 
s2*s3*s2*s3, s0*s1*s0*s1*s0*s1*s0*s1, 
s0*s1*s2*s1*s0*s1*s2*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*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*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