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Polytope of Type {218}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {218}*436
Also Known As : 218-gon, {218}. if this polytope has another name.
Group : SmallGroup(436,4)
Rank : 2
Schlafli Type : {218}
Number of vertices, edges, etc : 218, 218
Order of s0s1 : 218
Special Properties :
   Universal
   Spherical
   Locally Spherical
   Orientable
   Self-Dual
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   {218,2} of size 872
   {218,4} of size 1744
Vertex Figure Of :
   {2,218} of size 872
   {4,218} of size 1744
Quotients (Maximal Quotients in Boldface) :
   2-fold quotients : {109}*218
   109-fold quotients : {2}*4
Covers (Minimal Covers in Boldface) :
   2-fold covers : {436}*872
   3-fold covers : {654}*1308
   4-fold covers : {872}*1744
Permutation Representation (GAP) :
s0 := (  2,109)(  3,108)(  4,107)(  5,106)(  6,105)(  7,104)(  8,103)(  9,102)
( 10,101)( 11,100)( 12, 99)( 13, 98)( 14, 97)( 15, 96)( 16, 95)( 17, 94)
( 18, 93)( 19, 92)( 20, 91)( 21, 90)( 22, 89)( 23, 88)( 24, 87)( 25, 86)
( 26, 85)( 27, 84)( 28, 83)( 29, 82)( 30, 81)( 31, 80)( 32, 79)( 33, 78)
( 34, 77)( 35, 76)( 36, 75)( 37, 74)( 38, 73)( 39, 72)( 40, 71)( 41, 70)
( 42, 69)( 43, 68)( 44, 67)( 45, 66)( 46, 65)( 47, 64)( 48, 63)( 49, 62)
( 50, 61)( 51, 60)( 52, 59)( 53, 58)( 54, 57)( 55, 56)(111,218)(112,217)
(113,216)(114,215)(115,214)(116,213)(117,212)(118,211)(119,210)(120,209)
(121,208)(122,207)(123,206)(124,205)(125,204)(126,203)(127,202)(128,201)
(129,200)(130,199)(131,198)(132,197)(133,196)(134,195)(135,194)(136,193)
(137,192)(138,191)(139,190)(140,189)(141,188)(142,187)(143,186)(144,185)
(145,184)(146,183)(147,182)(148,181)(149,180)(150,179)(151,178)(152,177)
(153,176)(154,175)(155,174)(156,173)(157,172)(158,171)(159,170)(160,169)
(161,168)(162,167)(163,166)(164,165);;
s1 := (  1,111)(  2,110)(  3,218)(  4,217)(  5,216)(  6,215)(  7,214)(  8,213)
(  9,212)( 10,211)( 11,210)( 12,209)( 13,208)( 14,207)( 15,206)( 16,205)
( 17,204)( 18,203)( 19,202)( 20,201)( 21,200)( 22,199)( 23,198)( 24,197)
( 25,196)( 26,195)( 27,194)( 28,193)( 29,192)( 30,191)( 31,190)( 32,189)
( 33,188)( 34,187)( 35,186)( 36,185)( 37,184)( 38,183)( 39,182)( 40,181)
( 41,180)( 42,179)( 43,178)( 44,177)( 45,176)( 46,175)( 47,174)( 48,173)
( 49,172)( 50,171)( 51,170)( 52,169)( 53,168)( 54,167)( 55,166)( 56,165)
( 57,164)( 58,163)( 59,162)( 60,161)( 61,160)( 62,159)( 63,158)( 64,157)
( 65,156)( 66,155)( 67,154)( 68,153)( 69,152)( 70,151)( 71,150)( 72,149)
( 73,148)( 74,147)( 75,146)( 76,145)( 77,144)( 78,143)( 79,142)( 80,141)
( 81,140)( 82,139)( 83,138)( 84,137)( 85,136)( 86,135)( 87,134)( 88,133)
( 89,132)( 90,131)( 91,130)( 92,129)( 93,128)( 94,127)( 95,126)( 96,125)
( 97,124)( 98,123)( 99,122)(100,121)(101,120)(102,119)(103,118)(104,117)
(105,116)(106,115)(107,114)(108,113)(109,112);;
poly := Group([s0,s1]);;
 
Finitely Presented Group Representation (GAP) :
F := FreeGroup("s0","s1");;
s0 := F.1;;  s1 := F.2;;  
rels := [ s0*s0, s1*s1, s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1 ];;
poly := F / rels;;
 
Permutation Representation (Magma) :
s0 := Sym(218)!(  2,109)(  3,108)(  4,107)(  5,106)(  6,105)(  7,104)(  8,103)
(  9,102)( 10,101)( 11,100)( 12, 99)( 13, 98)( 14, 97)( 15, 96)( 16, 95)
( 17, 94)( 18, 93)( 19, 92)( 20, 91)( 21, 90)( 22, 89)( 23, 88)( 24, 87)
( 25, 86)( 26, 85)( 27, 84)( 28, 83)( 29, 82)( 30, 81)( 31, 80)( 32, 79)
( 33, 78)( 34, 77)( 35, 76)( 36, 75)( 37, 74)( 38, 73)( 39, 72)( 40, 71)
( 41, 70)( 42, 69)( 43, 68)( 44, 67)( 45, 66)( 46, 65)( 47, 64)( 48, 63)
( 49, 62)( 50, 61)( 51, 60)( 52, 59)( 53, 58)( 54, 57)( 55, 56)(111,218)
(112,217)(113,216)(114,215)(115,214)(116,213)(117,212)(118,211)(119,210)
(120,209)(121,208)(122,207)(123,206)(124,205)(125,204)(126,203)(127,202)
(128,201)(129,200)(130,199)(131,198)(132,197)(133,196)(134,195)(135,194)
(136,193)(137,192)(138,191)(139,190)(140,189)(141,188)(142,187)(143,186)
(144,185)(145,184)(146,183)(147,182)(148,181)(149,180)(150,179)(151,178)
(152,177)(153,176)(154,175)(155,174)(156,173)(157,172)(158,171)(159,170)
(160,169)(161,168)(162,167)(163,166)(164,165);
s1 := Sym(218)!(  1,111)(  2,110)(  3,218)(  4,217)(  5,216)(  6,215)(  7,214)
(  8,213)(  9,212)( 10,211)( 11,210)( 12,209)( 13,208)( 14,207)( 15,206)
( 16,205)( 17,204)( 18,203)( 19,202)( 20,201)( 21,200)( 22,199)( 23,198)
( 24,197)( 25,196)( 26,195)( 27,194)( 28,193)( 29,192)( 30,191)( 31,190)
( 32,189)( 33,188)( 34,187)( 35,186)( 36,185)( 37,184)( 38,183)( 39,182)
( 40,181)( 41,180)( 42,179)( 43,178)( 44,177)( 45,176)( 46,175)( 47,174)
( 48,173)( 49,172)( 50,171)( 51,170)( 52,169)( 53,168)( 54,167)( 55,166)
( 56,165)( 57,164)( 58,163)( 59,162)( 60,161)( 61,160)( 62,159)( 63,158)
( 64,157)( 65,156)( 66,155)( 67,154)( 68,153)( 69,152)( 70,151)( 71,150)
( 72,149)( 73,148)( 74,147)( 75,146)( 76,145)( 77,144)( 78,143)( 79,142)
( 80,141)( 81,140)( 82,139)( 83,138)( 84,137)( 85,136)( 86,135)( 87,134)
( 88,133)( 89,132)( 90,131)( 91,130)( 92,129)( 93,128)( 94,127)( 95,126)
( 96,125)( 97,124)( 98,123)( 99,122)(100,121)(101,120)(102,119)(103,118)
(104,117)(105,116)(106,115)(107,114)(108,113)(109,112);
poly := sub<Sym(218)|s0,s1>;
 
Finitely Presented Group Representation (Magma) :
poly<s0,s1> := Group< s0,s1 | s0*s0, s1*s1, s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1 >; 
 
References : None.
to this polytope