Polytope of Type {220}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {220}*440
Also Known As : 220-gon, {220}. if this polytope has another name.
Group : SmallGroup(440,36)
Rank : 2
Schlafli Type : {220}
Number of vertices, edges, etc : 220, 220
Order of s0s1 : 220
Special Properties :
Universal
Spherical
Locally Spherical
Orientable
Self-Dual
Related Polytopes :
Facet
Vertex Figure
Dual
Facet Of :
{220,2} of size 880
{220,4} of size 1760
Vertex Figure Of :
{2,220} of size 880
{4,220} of size 1760
Quotients (Maximal Quotients in Boldface) :
2-fold quotients : {110}*220
4-fold quotients : {55}*110
5-fold quotients : {44}*88
10-fold quotients : {22}*44
11-fold quotients : {20}*40
20-fold quotients : {11}*22
22-fold quotients : {10}*20
44-fold quotients : {5}*10
55-fold quotients : {4}*8
110-fold quotients : {2}*4
Covers (Minimal Covers in Boldface) :
2-fold covers : {440}*880
3-fold covers : {660}*1320
4-fold covers : {880}*1760
Permutation Representation (GAP) :
s0 := ( 2, 11)( 3, 10)( 4, 9)( 5, 8)( 6, 7)( 12, 45)( 13, 55)( 14, 54)
( 15, 53)( 16, 52)( 17, 51)( 18, 50)( 19, 49)( 20, 48)( 21, 47)( 22, 46)
( 23, 34)( 24, 44)( 25, 43)( 26, 42)( 27, 41)( 28, 40)( 29, 39)( 30, 38)
( 31, 37)( 32, 36)( 33, 35)( 57, 66)( 58, 65)( 59, 64)( 60, 63)( 61, 62)
( 67,100)( 68,110)( 69,109)( 70,108)( 71,107)( 72,106)( 73,105)( 74,104)
( 75,103)( 76,102)( 77,101)( 78, 89)( 79, 99)( 80, 98)( 81, 97)( 82, 96)
( 83, 95)( 84, 94)( 85, 93)( 86, 92)( 87, 91)( 88, 90)(111,166)(112,176)
(113,175)(114,174)(115,173)(116,172)(117,171)(118,170)(119,169)(120,168)
(121,167)(122,210)(123,220)(124,219)(125,218)(126,217)(127,216)(128,215)
(129,214)(130,213)(131,212)(132,211)(133,199)(134,209)(135,208)(136,207)
(137,206)(138,205)(139,204)(140,203)(141,202)(142,201)(143,200)(144,188)
(145,198)(146,197)(147,196)(148,195)(149,194)(150,193)(151,192)(152,191)
(153,190)(154,189)(155,177)(156,187)(157,186)(158,185)(159,184)(160,183)
(161,182)(162,181)(163,180)(164,179)(165,178);;
s1 := ( 1,123)( 2,122)( 3,132)( 4,131)( 5,130)( 6,129)( 7,128)( 8,127)
( 9,126)( 10,125)( 11,124)( 12,112)( 13,111)( 14,121)( 15,120)( 16,119)
( 17,118)( 18,117)( 19,116)( 20,115)( 21,114)( 22,113)( 23,156)( 24,155)
( 25,165)( 26,164)( 27,163)( 28,162)( 29,161)( 30,160)( 31,159)( 32,158)
( 33,157)( 34,145)( 35,144)( 36,154)( 37,153)( 38,152)( 39,151)( 40,150)
( 41,149)( 42,148)( 43,147)( 44,146)( 45,134)( 46,133)( 47,143)( 48,142)
( 49,141)( 50,140)( 51,139)( 52,138)( 53,137)( 54,136)( 55,135)( 56,178)
( 57,177)( 58,187)( 59,186)( 60,185)( 61,184)( 62,183)( 63,182)( 64,181)
( 65,180)( 66,179)( 67,167)( 68,166)( 69,176)( 70,175)( 71,174)( 72,173)
( 73,172)( 74,171)( 75,170)( 76,169)( 77,168)( 78,211)( 79,210)( 80,220)
( 81,219)( 82,218)( 83,217)( 84,216)( 85,215)( 86,214)( 87,213)( 88,212)
( 89,200)( 90,199)( 91,209)( 92,208)( 93,207)( 94,206)( 95,205)( 96,204)
( 97,203)( 98,202)( 99,201)(100,189)(101,188)(102,198)(103,197)(104,196)
(105,195)(106,194)(107,193)(108,192)(109,191)(110,190);;
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*s0*s1*s0*s1 ];;
poly := F / rels;;
Permutation Representation (Magma) :
s0 := Sym(220)!( 2, 11)( 3, 10)( 4, 9)( 5, 8)( 6, 7)( 12, 45)( 13, 55)
( 14, 54)( 15, 53)( 16, 52)( 17, 51)( 18, 50)( 19, 49)( 20, 48)( 21, 47)
( 22, 46)( 23, 34)( 24, 44)( 25, 43)( 26, 42)( 27, 41)( 28, 40)( 29, 39)
( 30, 38)( 31, 37)( 32, 36)( 33, 35)( 57, 66)( 58, 65)( 59, 64)( 60, 63)
( 61, 62)( 67,100)( 68,110)( 69,109)( 70,108)( 71,107)( 72,106)( 73,105)
( 74,104)( 75,103)( 76,102)( 77,101)( 78, 89)( 79, 99)( 80, 98)( 81, 97)
( 82, 96)( 83, 95)( 84, 94)( 85, 93)( 86, 92)( 87, 91)( 88, 90)(111,166)
(112,176)(113,175)(114,174)(115,173)(116,172)(117,171)(118,170)(119,169)
(120,168)(121,167)(122,210)(123,220)(124,219)(125,218)(126,217)(127,216)
(128,215)(129,214)(130,213)(131,212)(132,211)(133,199)(134,209)(135,208)
(136,207)(137,206)(138,205)(139,204)(140,203)(141,202)(142,201)(143,200)
(144,188)(145,198)(146,197)(147,196)(148,195)(149,194)(150,193)(151,192)
(152,191)(153,190)(154,189)(155,177)(156,187)(157,186)(158,185)(159,184)
(160,183)(161,182)(162,181)(163,180)(164,179)(165,178);
s1 := Sym(220)!( 1,123)( 2,122)( 3,132)( 4,131)( 5,130)( 6,129)( 7,128)
( 8,127)( 9,126)( 10,125)( 11,124)( 12,112)( 13,111)( 14,121)( 15,120)
( 16,119)( 17,118)( 18,117)( 19,116)( 20,115)( 21,114)( 22,113)( 23,156)
( 24,155)( 25,165)( 26,164)( 27,163)( 28,162)( 29,161)( 30,160)( 31,159)
( 32,158)( 33,157)( 34,145)( 35,144)( 36,154)( 37,153)( 38,152)( 39,151)
( 40,150)( 41,149)( 42,148)( 43,147)( 44,146)( 45,134)( 46,133)( 47,143)
( 48,142)( 49,141)( 50,140)( 51,139)( 52,138)( 53,137)( 54,136)( 55,135)
( 56,178)( 57,177)( 58,187)( 59,186)( 60,185)( 61,184)( 62,183)( 63,182)
( 64,181)( 65,180)( 66,179)( 67,167)( 68,166)( 69,176)( 70,175)( 71,174)
( 72,173)( 73,172)( 74,171)( 75,170)( 76,169)( 77,168)( 78,211)( 79,210)
( 80,220)( 81,219)( 82,218)( 83,217)( 84,216)( 85,215)( 86,214)( 87,213)
( 88,212)( 89,200)( 90,199)( 91,209)( 92,208)( 93,207)( 94,206)( 95,205)
( 96,204)( 97,203)( 98,202)( 99,201)(100,189)(101,188)(102,198)(103,197)
(104,196)(105,195)(106,194)(107,193)(108,192)(109,191)(110,190);
poly := sub<Sym(220)|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*s0*s1*s0*s1 >;
References : None.
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