Polytope of Type {214}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {214}*428
Also Known As : 214-gon, {214}. if this polytope has another name.
Group : SmallGroup(428,3)
Rank : 2
Schlafli Type : {214}
Number of vertices, edges, etc : 214, 214
Order of s0s1 : 214
Special Properties :
Universal
Spherical
Locally Spherical
Orientable
Self-Dual
Related Polytopes :
Facet
Vertex Figure
Dual
Facet Of :
{214,2} of size 856
{214,4} of size 1712
Vertex Figure Of :
{2,214} of size 856
{4,214} of size 1712
Quotients (Maximal Quotients in Boldface) :
2-fold quotients : {107}*214
107-fold quotients : {2}*4
Covers (Minimal Covers in Boldface) :
2-fold covers : {428}*856
3-fold covers : {642}*1284
4-fold covers : {856}*1712
Permutation Representation (GAP) :
s0 := ( 2,107)( 3,106)( 4,105)( 5,104)( 6,103)( 7,102)( 8,101)( 9,100)
( 10, 99)( 11, 98)( 12, 97)( 13, 96)( 14, 95)( 15, 94)( 16, 93)( 17, 92)
( 18, 91)( 19, 90)( 20, 89)( 21, 88)( 22, 87)( 23, 86)( 24, 85)( 25, 84)
( 26, 83)( 27, 82)( 28, 81)( 29, 80)( 30, 79)( 31, 78)( 32, 77)( 33, 76)
( 34, 75)( 35, 74)( 36, 73)( 37, 72)( 38, 71)( 39, 70)( 40, 69)( 41, 68)
( 42, 67)( 43, 66)( 44, 65)( 45, 64)( 46, 63)( 47, 62)( 48, 61)( 49, 60)
( 50, 59)( 51, 58)( 52, 57)( 53, 56)( 54, 55)(109,214)(110,213)(111,212)
(112,211)(113,210)(114,209)(115,208)(116,207)(117,206)(118,205)(119,204)
(120,203)(121,202)(122,201)(123,200)(124,199)(125,198)(126,197)(127,196)
(128,195)(129,194)(130,193)(131,192)(132,191)(133,190)(134,189)(135,188)
(136,187)(137,186)(138,185)(139,184)(140,183)(141,182)(142,181)(143,180)
(144,179)(145,178)(146,177)(147,176)(148,175)(149,174)(150,173)(151,172)
(152,171)(153,170)(154,169)(155,168)(156,167)(157,166)(158,165)(159,164)
(160,163)(161,162);;
s1 := ( 1,109)( 2,108)( 3,214)( 4,213)( 5,212)( 6,211)( 7,210)( 8,209)
( 9,208)( 10,207)( 11,206)( 12,205)( 13,204)( 14,203)( 15,202)( 16,201)
( 17,200)( 18,199)( 19,198)( 20,197)( 21,196)( 22,195)( 23,194)( 24,193)
( 25,192)( 26,191)( 27,190)( 28,189)( 29,188)( 30,187)( 31,186)( 32,185)
( 33,184)( 34,183)( 35,182)( 36,181)( 37,180)( 38,179)( 39,178)( 40,177)
( 41,176)( 42,175)( 43,174)( 44,173)( 45,172)( 46,171)( 47,170)( 48,169)
( 49,168)( 50,167)( 51,166)( 52,165)( 53,164)( 54,163)( 55,162)( 56,161)
( 57,160)( 58,159)( 59,158)( 60,157)( 61,156)( 62,155)( 63,154)( 64,153)
( 65,152)( 66,151)( 67,150)( 68,149)( 69,148)( 70,147)( 71,146)( 72,145)
( 73,144)( 74,143)( 75,142)( 76,141)( 77,140)( 78,139)( 79,138)( 80,137)
( 81,136)( 82,135)( 83,134)( 84,133)( 85,132)( 86,131)( 87,130)( 88,129)
( 89,128)( 90,127)( 91,126)( 92,125)( 93,124)( 94,123)( 95,122)( 96,121)
( 97,120)( 98,119)( 99,118)(100,117)(101,116)(102,115)(103,114)(104,113)
(105,112)(106,111)(107,110);;
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 ];;
poly := F / rels;;
Permutation Representation (Magma) :
s0 := Sym(214)!( 2,107)( 3,106)( 4,105)( 5,104)( 6,103)( 7,102)( 8,101)
( 9,100)( 10, 99)( 11, 98)( 12, 97)( 13, 96)( 14, 95)( 15, 94)( 16, 93)
( 17, 92)( 18, 91)( 19, 90)( 20, 89)( 21, 88)( 22, 87)( 23, 86)( 24, 85)
( 25, 84)( 26, 83)( 27, 82)( 28, 81)( 29, 80)( 30, 79)( 31, 78)( 32, 77)
( 33, 76)( 34, 75)( 35, 74)( 36, 73)( 37, 72)( 38, 71)( 39, 70)( 40, 69)
( 41, 68)( 42, 67)( 43, 66)( 44, 65)( 45, 64)( 46, 63)( 47, 62)( 48, 61)
( 49, 60)( 50, 59)( 51, 58)( 52, 57)( 53, 56)( 54, 55)(109,214)(110,213)
(111,212)(112,211)(113,210)(114,209)(115,208)(116,207)(117,206)(118,205)
(119,204)(120,203)(121,202)(122,201)(123,200)(124,199)(125,198)(126,197)
(127,196)(128,195)(129,194)(130,193)(131,192)(132,191)(133,190)(134,189)
(135,188)(136,187)(137,186)(138,185)(139,184)(140,183)(141,182)(142,181)
(143,180)(144,179)(145,178)(146,177)(147,176)(148,175)(149,174)(150,173)
(151,172)(152,171)(153,170)(154,169)(155,168)(156,167)(157,166)(158,165)
(159,164)(160,163)(161,162);
s1 := Sym(214)!( 1,109)( 2,108)( 3,214)( 4,213)( 5,212)( 6,211)( 7,210)
( 8,209)( 9,208)( 10,207)( 11,206)( 12,205)( 13,204)( 14,203)( 15,202)
( 16,201)( 17,200)( 18,199)( 19,198)( 20,197)( 21,196)( 22,195)( 23,194)
( 24,193)( 25,192)( 26,191)( 27,190)( 28,189)( 29,188)( 30,187)( 31,186)
( 32,185)( 33,184)( 34,183)( 35,182)( 36,181)( 37,180)( 38,179)( 39,178)
( 40,177)( 41,176)( 42,175)( 43,174)( 44,173)( 45,172)( 46,171)( 47,170)
( 48,169)( 49,168)( 50,167)( 51,166)( 52,165)( 53,164)( 54,163)( 55,162)
( 56,161)( 57,160)( 58,159)( 59,158)( 60,157)( 61,156)( 62,155)( 63,154)
( 64,153)( 65,152)( 66,151)( 67,150)( 68,149)( 69,148)( 70,147)( 71,146)
( 72,145)( 73,144)( 74,143)( 75,142)( 76,141)( 77,140)( 78,139)( 79,138)
( 80,137)( 81,136)( 82,135)( 83,134)( 84,133)( 85,132)( 86,131)( 87,130)
( 88,129)( 89,128)( 90,127)( 91,126)( 92,125)( 93,124)( 94,123)( 95,122)
( 96,121)( 97,120)( 98,119)( 99,118)(100,117)(101,116)(102,115)(103,114)
(104,113)(105,112)(106,111)(107,110);
poly := sub<Sym(214)|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 >;
References : None.
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