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Polytope of Type {2,280}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,280}*1120
if this polytope has a name.
Group : SmallGroup(1120,839)
Rank : 3
Schlafli Type : {2,280}
Number of vertices, edges, etc : 2, 280, 280
Order of s0s1s2 : 280
Order of s0s1s2s1 : 2
Special Properties :
   Degenerate
   Universal
   Compact Hyperbolic Quotient
   Locally Spherical
   Orientable
   Flat
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   None in this Atlas
Vertex Figure Of :
   None in this Atlas
Quotients (Maximal Quotients in Boldface) :
   2-fold quotients : {2,140}*560
   4-fold quotients : {2,70}*280
   5-fold quotients : {2,56}*224
   7-fold quotients : {2,40}*160
   8-fold quotients : {2,35}*140
   10-fold quotients : {2,28}*112
   14-fold quotients : {2,20}*80
   20-fold quotients : {2,14}*56
   28-fold quotients : {2,10}*40
   35-fold quotients : {2,8}*32
   40-fold quotients : {2,7}*28
   56-fold quotients : {2,5}*20
   70-fold quotients : {2,4}*16
   140-fold quotients : {2,2}*8
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :
s0 := (1,2);;
s1 := (  4,  9)(  5,  8)(  6,  7)( 10, 31)( 11, 37)( 12, 36)( 13, 35)( 14, 34)
( 15, 33)( 16, 32)( 17, 24)( 18, 30)( 19, 29)( 20, 28)( 21, 27)( 22, 26)
( 23, 25)( 39, 44)( 40, 43)( 41, 42)( 45, 66)( 46, 72)( 47, 71)( 48, 70)
( 49, 69)( 50, 68)( 51, 67)( 52, 59)( 53, 65)( 54, 64)( 55, 63)( 56, 62)
( 57, 61)( 58, 60)( 73,108)( 74,114)( 75,113)( 76,112)( 77,111)( 78,110)
( 79,109)( 80,136)( 81,142)( 82,141)( 83,140)( 84,139)( 85,138)( 86,137)
( 87,129)( 88,135)( 89,134)( 90,133)( 91,132)( 92,131)( 93,130)( 94,122)
( 95,128)( 96,127)( 97,126)( 98,125)( 99,124)(100,123)(101,115)(102,121)
(103,120)(104,119)(105,118)(106,117)(107,116)(143,213)(144,219)(145,218)
(146,217)(147,216)(148,215)(149,214)(150,241)(151,247)(152,246)(153,245)
(154,244)(155,243)(156,242)(157,234)(158,240)(159,239)(160,238)(161,237)
(162,236)(163,235)(164,227)(165,233)(166,232)(167,231)(168,230)(169,229)
(170,228)(171,220)(172,226)(173,225)(174,224)(175,223)(176,222)(177,221)
(178,248)(179,254)(180,253)(181,252)(182,251)(183,250)(184,249)(185,276)
(186,282)(187,281)(188,280)(189,279)(190,278)(191,277)(192,269)(193,275)
(194,274)(195,273)(196,272)(197,271)(198,270)(199,262)(200,268)(201,267)
(202,266)(203,265)(204,264)(205,263)(206,255)(207,261)(208,260)(209,259)
(210,258)(211,257)(212,256);;
s2 := (  3,151)(  4,150)(  5,156)(  6,155)(  7,154)(  8,153)(  9,152)( 10,144)
( 11,143)( 12,149)( 13,148)( 14,147)( 15,146)( 16,145)( 17,172)( 18,171)
( 19,177)( 20,176)( 21,175)( 22,174)( 23,173)( 24,165)( 25,164)( 26,170)
( 27,169)( 28,168)( 29,167)( 30,166)( 31,158)( 32,157)( 33,163)( 34,162)
( 35,161)( 36,160)( 37,159)( 38,186)( 39,185)( 40,191)( 41,190)( 42,189)
( 43,188)( 44,187)( 45,179)( 46,178)( 47,184)( 48,183)( 49,182)( 50,181)
( 51,180)( 52,207)( 53,206)( 54,212)( 55,211)( 56,210)( 57,209)( 58,208)
( 59,200)( 60,199)( 61,205)( 62,204)( 63,203)( 64,202)( 65,201)( 66,193)
( 67,192)( 68,198)( 69,197)( 70,196)( 71,195)( 72,194)( 73,256)( 74,255)
( 75,261)( 76,260)( 77,259)( 78,258)( 79,257)( 80,249)( 81,248)( 82,254)
( 83,253)( 84,252)( 85,251)( 86,250)( 87,277)( 88,276)( 89,282)( 90,281)
( 91,280)( 92,279)( 93,278)( 94,270)( 95,269)( 96,275)( 97,274)( 98,273)
( 99,272)(100,271)(101,263)(102,262)(103,268)(104,267)(105,266)(106,265)
(107,264)(108,221)(109,220)(110,226)(111,225)(112,224)(113,223)(114,222)
(115,214)(116,213)(117,219)(118,218)(119,217)(120,216)(121,215)(122,242)
(123,241)(124,247)(125,246)(126,245)(127,244)(128,243)(129,235)(130,234)
(131,240)(132,239)(133,238)(134,237)(135,236)(136,228)(137,227)(138,233)
(139,232)(140,231)(141,230)(142,229);;
poly := Group([s0,s1,s2]);;
 
Finitely Presented Group Representation (GAP) :
F := FreeGroup("s0","s1","s2");;
s0 := F.1;;  s1 := F.2;;  s2 := F.3;;  
rels := [ s0*s0, s1*s1, s2*s2, s0*s1*s0*s1, s0*s2*s0*s2, 
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2 ];;
poly := F / rels;;
 
Permutation Representation (Magma) :
s0 := Sym(282)!(1,2);
s1 := Sym(282)!(  4,  9)(  5,  8)(  6,  7)( 10, 31)( 11, 37)( 12, 36)( 13, 35)
( 14, 34)( 15, 33)( 16, 32)( 17, 24)( 18, 30)( 19, 29)( 20, 28)( 21, 27)
( 22, 26)( 23, 25)( 39, 44)( 40, 43)( 41, 42)( 45, 66)( 46, 72)( 47, 71)
( 48, 70)( 49, 69)( 50, 68)( 51, 67)( 52, 59)( 53, 65)( 54, 64)( 55, 63)
( 56, 62)( 57, 61)( 58, 60)( 73,108)( 74,114)( 75,113)( 76,112)( 77,111)
( 78,110)( 79,109)( 80,136)( 81,142)( 82,141)( 83,140)( 84,139)( 85,138)
( 86,137)( 87,129)( 88,135)( 89,134)( 90,133)( 91,132)( 92,131)( 93,130)
( 94,122)( 95,128)( 96,127)( 97,126)( 98,125)( 99,124)(100,123)(101,115)
(102,121)(103,120)(104,119)(105,118)(106,117)(107,116)(143,213)(144,219)
(145,218)(146,217)(147,216)(148,215)(149,214)(150,241)(151,247)(152,246)
(153,245)(154,244)(155,243)(156,242)(157,234)(158,240)(159,239)(160,238)
(161,237)(162,236)(163,235)(164,227)(165,233)(166,232)(167,231)(168,230)
(169,229)(170,228)(171,220)(172,226)(173,225)(174,224)(175,223)(176,222)
(177,221)(178,248)(179,254)(180,253)(181,252)(182,251)(183,250)(184,249)
(185,276)(186,282)(187,281)(188,280)(189,279)(190,278)(191,277)(192,269)
(193,275)(194,274)(195,273)(196,272)(197,271)(198,270)(199,262)(200,268)
(201,267)(202,266)(203,265)(204,264)(205,263)(206,255)(207,261)(208,260)
(209,259)(210,258)(211,257)(212,256);
s2 := Sym(282)!(  3,151)(  4,150)(  5,156)(  6,155)(  7,154)(  8,153)(  9,152)
( 10,144)( 11,143)( 12,149)( 13,148)( 14,147)( 15,146)( 16,145)( 17,172)
( 18,171)( 19,177)( 20,176)( 21,175)( 22,174)( 23,173)( 24,165)( 25,164)
( 26,170)( 27,169)( 28,168)( 29,167)( 30,166)( 31,158)( 32,157)( 33,163)
( 34,162)( 35,161)( 36,160)( 37,159)( 38,186)( 39,185)( 40,191)( 41,190)
( 42,189)( 43,188)( 44,187)( 45,179)( 46,178)( 47,184)( 48,183)( 49,182)
( 50,181)( 51,180)( 52,207)( 53,206)( 54,212)( 55,211)( 56,210)( 57,209)
( 58,208)( 59,200)( 60,199)( 61,205)( 62,204)( 63,203)( 64,202)( 65,201)
( 66,193)( 67,192)( 68,198)( 69,197)( 70,196)( 71,195)( 72,194)( 73,256)
( 74,255)( 75,261)( 76,260)( 77,259)( 78,258)( 79,257)( 80,249)( 81,248)
( 82,254)( 83,253)( 84,252)( 85,251)( 86,250)( 87,277)( 88,276)( 89,282)
( 90,281)( 91,280)( 92,279)( 93,278)( 94,270)( 95,269)( 96,275)( 97,274)
( 98,273)( 99,272)(100,271)(101,263)(102,262)(103,268)(104,267)(105,266)
(106,265)(107,264)(108,221)(109,220)(110,226)(111,225)(112,224)(113,223)
(114,222)(115,214)(116,213)(117,219)(118,218)(119,217)(120,216)(121,215)
(122,242)(123,241)(124,247)(125,246)(126,245)(127,244)(128,243)(129,235)
(130,234)(131,240)(132,239)(133,238)(134,237)(135,236)(136,228)(137,227)
(138,233)(139,232)(140,231)(141,230)(142,229);
poly := sub<Sym(282)|s0,s1,s2>;
 
Finitely Presented Group Representation (Magma) :
poly<s0,s1,s2> := Group< s0,s1,s2 | s0*s0, s1*s1, s2*s2, 
s0*s1*s0*s1, s0*s2*s0*s2, s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2 >; 
 

to this polytope