Questions?
See the FAQ
or other info.

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
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