Polytope of Type {284}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {284}*568
Also Known As : 284-gon, {284}. if this polytope has another name.
Group : SmallGroup(568,5)
Rank : 2
Schlafli Type : {284}
Number of vertices, edges, etc : 284, 284
Order of s0s1 : 284
Special Properties :
Universal
Spherical
Locally Spherical
Orientable
Self-Dual
Related Polytopes :
Facet
Vertex Figure
Dual
Facet Of :
{284,2} of size 1136
Vertex Figure Of :
{2,284} of size 1136
Quotients (Maximal Quotients in Boldface) :
2-fold quotients : {142}*284
4-fold quotients : {71}*142
71-fold quotients : {4}*8
142-fold quotients : {2}*4
Covers (Minimal Covers in Boldface) :
2-fold covers : {568}*1136
3-fold covers : {852}*1704
Irregular Quotients (of which this is a minimal cover):
None.
Permutation Representation (GAP) :
s0 := ( 2, 71)( 3, 70)( 4, 69)( 5, 68)( 6, 67)( 7, 66)( 8, 65)( 9, 64)( 10, 63)( 11, 62)( 12, 61)( 13, 60)( 14, 59)( 15, 58)( 16, 57)( 17, 56)( 18, 55)( 19, 54)( 20, 53)( 21, 52)( 22, 51)( 23, 50)( 24, 49)( 25, 48)( 26, 47)( 27, 46)( 28, 45)( 29, 44)( 30, 43)( 31, 42)( 32, 41)( 33, 40)( 34, 39)( 35, 38)( 36, 37)( 73,142)( 74,141)( 75,140)( 76,139)( 77,138)( 78,137)( 79,136)( 80,135)( 81,134)( 82,133)( 83,132)( 84,131)( 85,130)( 86,129)( 87,128)( 88,127)( 89,126)( 90,125)( 91,124)( 92,123)( 93,122)( 94,121)( 95,120)( 96,119)( 97,118)( 98,117)( 99,116)(100,115)(101,114)(102,113)(103,112)(104,111)(105,110)(106,109)(107,108)(143,214)(144,284)(145,283)(146,282)(147,281)(148,280)(149,279)(150,278)(151,277)(152,276)(153,275)(154,274)(155,273)(156,272)(157,271)(158,270)(159,269)(160,268)(161,267)(162,266)(163,265)(164,264)(165,263)(166,262)(167,261)(168,260)(169,259)(170,258)(171,257)(172,256)(173,255)(174,254)(175,253)(176,252)(177,251)(178,250)(179,249)(180,248)(181,247)(182,246)(183,245)(184,244)(185,243)(186,242)(187,241)(188,240)(189,239)(190,238)(191,237)(192,236)(193,235)(194,234)(195,233)(196,232)(197,231)(198,230)(199,229)(200,228)(201,227)(202,226)(203,225)(204,224)(205,223)(206,222)(207,221)(208,220)(209,219)(210,218)(211,217)(212,216)(213,215);;
s1 := ( 1,144)( 2,143)( 3,213)( 4,212)( 5,211)( 6,210)( 7,209)( 8,208)( 9,207)( 10,206)( 11,205)( 12,204)( 13,203)( 14,202)( 15,201)( 16,200)( 17,199)( 18,198)( 19,197)( 20,196)( 21,195)( 22,194)( 23,193)( 24,192)( 25,191)( 26,190)( 27,189)( 28,188)( 29,187)( 30,186)( 31,185)( 32,184)( 33,183)( 34,182)( 35,181)( 36,180)( 37,179)( 38,178)( 39,177)( 40,176)( 41,175)( 42,174)( 43,173)( 44,172)( 45,171)( 46,170)( 47,169)( 48,168)( 49,167)( 50,166)( 51,165)( 52,164)( 53,163)( 54,162)( 55,161)( 56,160)( 57,159)( 58,158)( 59,157)( 60,156)( 61,155)( 62,154)( 63,153)( 64,152)( 65,151)( 66,150)( 67,149)( 68,148)( 69,147)( 70,146)( 71,145)( 72,215)( 73,214)( 74,284)( 75,283)( 76,282)( 77,281)( 78,280)( 79,279)( 80,278)( 81,277)( 82,276)( 83,275)( 84,274)( 85,273)( 86,272)( 87,271)( 88,270)( 89,269)( 90,268)( 91,267)( 92,266)( 93,265)( 94,264)( 95,263)( 96,262)( 97,261)( 98,260)( 99,259)(100,258)(101,257)(102,256)(103,255)(104,254)(105,253)(106,252)(107,251)(108,250)(109,249)(110,248)(111,247)(112,246)(113,245)(114,244)(115,243)(116,242)(117,241)(118,240)(119,239)(120,238)(121,237)(122,236)(123,235)(124,234)(125,233)(126,232)(127,231)(128,230)(129,229)(130,228)(131,227)(132,226)(133,225)(134,224)(135,223)(136,222)(137,221)(138,220)(139,219)(140,218)(141,217)(142,216);;
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*s0*s1*s0*s1*s0*s1*s0*s1 ];;
poly := F / rels;;
Permutation Representation (Magma) :
s0 := Sym(284)!( 2, 71)( 3, 70)( 4, 69)( 5, 68)( 6, 67)( 7, 66)( 8, 65)( 9, 64)( 10, 63)( 11, 62)( 12, 61)( 13, 60)( 14, 59)( 15, 58)( 16, 57)( 17, 56)( 18, 55)( 19, 54)( 20, 53)( 21, 52)( 22, 51)( 23, 50)( 24, 49)( 25, 48)( 26, 47)( 27, 46)( 28, 45)( 29, 44)( 30, 43)( 31, 42)( 32, 41)( 33, 40)( 34, 39)( 35, 38)( 36, 37)( 73,142)( 74,141)( 75,140)( 76,139)( 77,138)( 78,137)( 79,136)( 80,135)( 81,134)( 82,133)( 83,132)( 84,131)( 85,130)( 86,129)( 87,128)( 88,127)( 89,126)( 90,125)( 91,124)( 92,123)( 93,122)( 94,121)( 95,120)( 96,119)( 97,118)( 98,117)( 99,116)(100,115)(101,114)(102,113)(103,112)(104,111)(105,110)(106,109)(107,108)(143,214)(144,284)(145,283)(146,282)(147,281)(148,280)(149,279)(150,278)(151,277)(152,276)(153,275)(154,274)(155,273)(156,272)(157,271)(158,270)(159,269)(160,268)(161,267)(162,266)(163,265)(164,264)(165,263)(166,262)(167,261)(168,260)(169,259)(170,258)(171,257)(172,256)(173,255)(174,254)(175,253)(176,252)(177,251)(178,250)(179,249)(180,248)(181,247)(182,246)(183,245)(184,244)(185,243)(186,242)(187,241)(188,240)(189,239)(190,238)(191,237)(192,236)(193,235)(194,234)(195,233)(196,232)(197,231)(198,230)(199,229)(200,228)(201,227)(202,226)(203,225)(204,224)(205,223)(206,222)(207,221)(208,220)(209,219)(210,218)(211,217)(212,216)(213,215);
s1 := Sym(284)!( 1,144)( 2,143)( 3,213)( 4,212)( 5,211)( 6,210)( 7,209)( 8,208)( 9,207)( 10,206)( 11,205)( 12,204)( 13,203)( 14,202)( 15,201)( 16,200)( 17,199)( 18,198)( 19,197)( 20,196)( 21,195)( 22,194)( 23,193)( 24,192)( 25,191)( 26,190)( 27,189)( 28,188)( 29,187)( 30,186)( 31,185)( 32,184)( 33,183)( 34,182)( 35,181)( 36,180)( 37,179)( 38,178)( 39,177)( 40,176)( 41,175)( 42,174)( 43,173)( 44,172)( 45,171)( 46,170)( 47,169)( 48,168)( 49,167)( 50,166)( 51,165)( 52,164)( 53,163)( 54,162)( 55,161)( 56,160)( 57,159)( 58,158)( 59,157)( 60,156)( 61,155)( 62,154)( 63,153)( 64,152)( 65,151)( 66,150)( 67,149)( 68,148)( 69,147)( 70,146)( 71,145)( 72,215)( 73,214)( 74,284)( 75,283)( 76,282)( 77,281)( 78,280)( 79,279)( 80,278)( 81,277)( 82,276)( 83,275)( 84,274)( 85,273)( 86,272)( 87,271)( 88,270)( 89,269)( 90,268)( 91,267)( 92,266)( 93,265)( 94,264)( 95,263)( 96,262)( 97,261)( 98,260)( 99,259)(100,258)(101,257)(102,256)(103,255)(104,254)(105,253)(106,252)(107,251)(108,250)(109,249)(110,248)(111,247)(112,246)(113,245)(114,244)(115,243)(116,242)(117,241)(118,240)(119,239)(120,238)(121,237)(122,236)(123,235)(124,234)(125,233)(126,232)(127,231)(128,230)(129,229)(130,228)(131,227)(132,226)(133,225)(134,224)(135,223)(136,222)(137,221)(138,220)(139,219)(140,218)(141,217)(142,216);
poly := sub<Sym(284)|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*s0*s1*s0*s1*s0*s1*s0*s1 >;
References : None.
to this polytope