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Polytope of Type {280}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {280}*560
Also Known As : 280-gon, {280}. if this polytope has another name.
Group : SmallGroup(560,67)
Rank : 2
Schlafli Type : {280}
Number of vertices, edges, etc : 280, 280
Order of s0s1 : 280
Special Properties :
   Universal
   Spherical
   Locally Spherical
   Orientable
   Self-Dual
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   {280,2} of size 1120
Vertex Figure Of :
   {2,280} of size 1120
Quotients (Maximal Quotients in Boldface) :
   2-fold quotients : {140}*280
   4-fold quotients : {70}*140
   5-fold quotients : {56}*112
   7-fold quotients : {40}*80
   8-fold quotients : {35}*70
   10-fold quotients : {28}*56
   14-fold quotients : {20}*40
   20-fold quotients : {14}*28
   28-fold quotients : {10}*20
   35-fold quotients : {8}*16
   40-fold quotients : {7}*14
   56-fold quotients : {5}*10
   70-fold quotients : {4}*8
   140-fold quotients : {2}*4
Covers (Minimal Covers in Boldface) :
   2-fold covers : {560}*1120
   3-fold covers : {840}*1680
Permutation Representation (GAP) :
s0 := (  2,  7)(  3,  6)(  4,  5)(  8, 29)(  9, 35)( 10, 34)( 11, 33)( 12, 32)
( 13, 31)( 14, 30)( 15, 22)( 16, 28)( 17, 27)( 18, 26)( 19, 25)( 20, 24)
( 21, 23)( 37, 42)( 38, 41)( 39, 40)( 43, 64)( 44, 70)( 45, 69)( 46, 68)
( 47, 67)( 48, 66)( 49, 65)( 50, 57)( 51, 63)( 52, 62)( 53, 61)( 54, 60)
( 55, 59)( 56, 58)( 71,106)( 72,112)( 73,111)( 74,110)( 75,109)( 76,108)
( 77,107)( 78,134)( 79,140)( 80,139)( 81,138)( 82,137)( 83,136)( 84,135)
( 85,127)( 86,133)( 87,132)( 88,131)( 89,130)( 90,129)( 91,128)( 92,120)
( 93,126)( 94,125)( 95,124)( 96,123)( 97,122)( 98,121)( 99,113)(100,119)
(101,118)(102,117)(103,116)(104,115)(105,114)(141,211)(142,217)(143,216)
(144,215)(145,214)(146,213)(147,212)(148,239)(149,245)(150,244)(151,243)
(152,242)(153,241)(154,240)(155,232)(156,238)(157,237)(158,236)(159,235)
(160,234)(161,233)(162,225)(163,231)(164,230)(165,229)(166,228)(167,227)
(168,226)(169,218)(170,224)(171,223)(172,222)(173,221)(174,220)(175,219)
(176,246)(177,252)(178,251)(179,250)(180,249)(181,248)(182,247)(183,274)
(184,280)(185,279)(186,278)(187,277)(188,276)(189,275)(190,267)(191,273)
(192,272)(193,271)(194,270)(195,269)(196,268)(197,260)(198,266)(199,265)
(200,264)(201,263)(202,262)(203,261)(204,253)(205,259)(206,258)(207,257)
(208,256)(209,255)(210,254);;
s1 := (  1,149)(  2,148)(  3,154)(  4,153)(  5,152)(  6,151)(  7,150)(  8,142)
(  9,141)( 10,147)( 11,146)( 12,145)( 13,144)( 14,143)( 15,170)( 16,169)
( 17,175)( 18,174)( 19,173)( 20,172)( 21,171)( 22,163)( 23,162)( 24,168)
( 25,167)( 26,166)( 27,165)( 28,164)( 29,156)( 30,155)( 31,161)( 32,160)
( 33,159)( 34,158)( 35,157)( 36,184)( 37,183)( 38,189)( 39,188)( 40,187)
( 41,186)( 42,185)( 43,177)( 44,176)( 45,182)( 46,181)( 47,180)( 48,179)
( 49,178)( 50,205)( 51,204)( 52,210)( 53,209)( 54,208)( 55,207)( 56,206)
( 57,198)( 58,197)( 59,203)( 60,202)( 61,201)( 62,200)( 63,199)( 64,191)
( 65,190)( 66,196)( 67,195)( 68,194)( 69,193)( 70,192)( 71,254)( 72,253)
( 73,259)( 74,258)( 75,257)( 76,256)( 77,255)( 78,247)( 79,246)( 80,252)
( 81,251)( 82,250)( 83,249)( 84,248)( 85,275)( 86,274)( 87,280)( 88,279)
( 89,278)( 90,277)( 91,276)( 92,268)( 93,267)( 94,273)( 95,272)( 96,271)
( 97,270)( 98,269)( 99,261)(100,260)(101,266)(102,265)(103,264)(104,263)
(105,262)(106,219)(107,218)(108,224)(109,223)(110,222)(111,221)(112,220)
(113,212)(114,211)(115,217)(116,216)(117,215)(118,214)(119,213)(120,240)
(121,239)(122,245)(123,244)(124,243)(125,242)(126,241)(127,233)(128,232)
(129,238)(130,237)(131,236)(132,235)(133,234)(134,226)(135,225)(136,231)
(137,230)(138,229)(139,228)(140,227);;
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*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*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(280)!(  2,  7)(  3,  6)(  4,  5)(  8, 29)(  9, 35)( 10, 34)( 11, 33)
( 12, 32)( 13, 31)( 14, 30)( 15, 22)( 16, 28)( 17, 27)( 18, 26)( 19, 25)
( 20, 24)( 21, 23)( 37, 42)( 38, 41)( 39, 40)( 43, 64)( 44, 70)( 45, 69)
( 46, 68)( 47, 67)( 48, 66)( 49, 65)( 50, 57)( 51, 63)( 52, 62)( 53, 61)
( 54, 60)( 55, 59)( 56, 58)( 71,106)( 72,112)( 73,111)( 74,110)( 75,109)
( 76,108)( 77,107)( 78,134)( 79,140)( 80,139)( 81,138)( 82,137)( 83,136)
( 84,135)( 85,127)( 86,133)( 87,132)( 88,131)( 89,130)( 90,129)( 91,128)
( 92,120)( 93,126)( 94,125)( 95,124)( 96,123)( 97,122)( 98,121)( 99,113)
(100,119)(101,118)(102,117)(103,116)(104,115)(105,114)(141,211)(142,217)
(143,216)(144,215)(145,214)(146,213)(147,212)(148,239)(149,245)(150,244)
(151,243)(152,242)(153,241)(154,240)(155,232)(156,238)(157,237)(158,236)
(159,235)(160,234)(161,233)(162,225)(163,231)(164,230)(165,229)(166,228)
(167,227)(168,226)(169,218)(170,224)(171,223)(172,222)(173,221)(174,220)
(175,219)(176,246)(177,252)(178,251)(179,250)(180,249)(181,248)(182,247)
(183,274)(184,280)(185,279)(186,278)(187,277)(188,276)(189,275)(190,267)
(191,273)(192,272)(193,271)(194,270)(195,269)(196,268)(197,260)(198,266)
(199,265)(200,264)(201,263)(202,262)(203,261)(204,253)(205,259)(206,258)
(207,257)(208,256)(209,255)(210,254);
s1 := Sym(280)!(  1,149)(  2,148)(  3,154)(  4,153)(  5,152)(  6,151)(  7,150)
(  8,142)(  9,141)( 10,147)( 11,146)( 12,145)( 13,144)( 14,143)( 15,170)
( 16,169)( 17,175)( 18,174)( 19,173)( 20,172)( 21,171)( 22,163)( 23,162)
( 24,168)( 25,167)( 26,166)( 27,165)( 28,164)( 29,156)( 30,155)( 31,161)
( 32,160)( 33,159)( 34,158)( 35,157)( 36,184)( 37,183)( 38,189)( 39,188)
( 40,187)( 41,186)( 42,185)( 43,177)( 44,176)( 45,182)( 46,181)( 47,180)
( 48,179)( 49,178)( 50,205)( 51,204)( 52,210)( 53,209)( 54,208)( 55,207)
( 56,206)( 57,198)( 58,197)( 59,203)( 60,202)( 61,201)( 62,200)( 63,199)
( 64,191)( 65,190)( 66,196)( 67,195)( 68,194)( 69,193)( 70,192)( 71,254)
( 72,253)( 73,259)( 74,258)( 75,257)( 76,256)( 77,255)( 78,247)( 79,246)
( 80,252)( 81,251)( 82,250)( 83,249)( 84,248)( 85,275)( 86,274)( 87,280)
( 88,279)( 89,278)( 90,277)( 91,276)( 92,268)( 93,267)( 94,273)( 95,272)
( 96,271)( 97,270)( 98,269)( 99,261)(100,260)(101,266)(102,265)(103,264)
(104,263)(105,262)(106,219)(107,218)(108,224)(109,223)(110,222)(111,221)
(112,220)(113,212)(114,211)(115,217)(116,216)(117,215)(118,214)(119,213)
(120,240)(121,239)(122,245)(123,244)(124,243)(125,242)(126,241)(127,233)
(128,232)(129,238)(130,237)(131,236)(132,235)(133,234)(134,226)(135,225)
(136,231)(137,230)(138,229)(139,228)(140,227);
poly := sub<Sym(280)|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*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*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