Polytope of Type {4,102}

Play with this polytope as a twisty puzzle

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {4,102}*816a
Also Known As : {4,102|2}. if this polytope has another name.
Group : SmallGroup(816,175)
Rank : 3
Schlafli Type : {4,102}
Number of vertices, edges, etc : 4, 204, 102
Order of s0s1s2 : 204
Order of s0s1s2s1 : 2
Special Properties :
   Compact Hyperbolic Quotient
   Locally Spherical
   Orientable
   Flat
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   {4,102,2} of size 1632
Vertex Figure Of :
   {2,4,102} of size 1632
Quotients (Maximal Quotients in Boldface) :
   2-fold quotients : {2,102}*408
   3-fold quotients : {4,34}*272
   4-fold quotients : {2,51}*204
   6-fold quotients : {2,34}*136
   12-fold quotients : {2,17}*68
   17-fold quotients : {4,6}*48a
   34-fold quotients : {2,6}*24
   51-fold quotients : {4,2}*16
   68-fold quotients : {2,3}*12
   102-fold quotients : {2,2}*8
Covers (Minimal Covers in Boldface) :
   2-fold covers : {4,204}*1632a, {8,102}*1632
Irregular Quotients (of which this is a minimal cover):
   None.

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);;
poly := Group([s0,s1,s2]);;
Finitely Presented Group Representation (GAP) : 
F := FreeGroup("s0","s1","s2");;
s0 := F.1;;  s1 := F.2;;  s2 := F.3;;  
rels := [ s0*s0, s1*s1, s2*s2, s0*s2*s0*s2, 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(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)(  2,119)(  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(204)!(  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);
poly := sub<Sym(204)|s0,s1,s2>;
Finitely Presented Group Representation (Magma) : 
poly<s0,s1,s2> := Group< s0,s1,s2 | s0*s0, s1*s1, s2*s2, 
s0*s2*s0*s2, 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 >;
References : None.
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