Polytope of Type {140,4}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {140,4}*1120
Also Known As : {140,4|2}. if this polytope has another name.
Group : SmallGroup(1120,819)
Rank : 3
Schlafli Type : {140,4}
Number of vertices, edges, etc : 140, 280, 4
Order of s₀s₁s₂ : 140
Order of s₀s₁s₂s₁ : 2
Special Properties :
   Compact Hyperbolic Quotient
   Locally Spherical
   Orientable
   Flat
   Self-Petrie
Related Polytopes :
   Facet
   Vertex Figure
   Dual
   Petrial
   Skewing Operation
Facet Of :
   None in this Atlas
Vertex Figure Of :
   None in this Atlas
Quotients (Maximal Quotients in Boldface) :
   2-fold quotients : {140,2}*560, {70,4}*560
   4-fold quotients : {70,2}*280
   5-fold quotients : {28,4}*224
   7-fold quotients : {20,4}*160
   8-fold quotients : {35,2}*140
   10-fold quotients : {28,2}*112, {14,4}*112
   14-fold quotients : {20,2}*80, {10,4}*80
   20-fold quotients : {14,2}*56
   28-fold quotients : {10,2}*40
   35-fold quotients : {4,4}*32
   40-fold quotients : {7,2}*28
   56-fold quotients : {5,2}*20
   70-fold quotients : {2,4}*16, {4,2}*16
   140-fold quotients : {2,2}*8
Covers (Minimal Covers in Boldface) :
   None in this atlas.
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)( 72, 77)( 73, 76)( 74, 75)( 78, 99)( 79,105)( 80,104)
( 81,103)( 82,102)( 83,101)( 84,100)( 85, 92)( 86, 98)( 87, 97)( 88, 96)
( 89, 95)( 90, 94)( 91, 93)(107,112)(108,111)(109,110)(113,134)(114,140)
(115,139)(116,138)(117,137)(118,136)(119,135)(120,127)(121,133)(122,132)
(123,131)(124,130)(125,129)(126,128)(141,176)(142,182)(143,181)(144,180)
(145,179)(146,178)(147,177)(148,204)(149,210)(150,209)(151,208)(152,207)
(153,206)(154,205)(155,197)(156,203)(157,202)(158,201)(159,200)(160,199)
(161,198)(162,190)(163,196)(164,195)(165,194)(166,193)(167,192)(168,191)
(169,183)(170,189)(171,188)(172,187)(173,186)(174,185)(175,184)(211,246)
(212,252)(213,251)(214,250)(215,249)(216,248)(217,247)(218,274)(219,280)
(220,279)(221,278)(222,277)(223,276)(224,275)(225,267)(226,273)(227,272)
(228,271)(229,270)(230,269)(231,268)(232,260)(233,266)(234,265)(235,264)
(236,263)(237,262)(238,261)(239,253)(240,259)(241,258)(242,257)(243,256)
(244,255)(245,254);;
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)( 71,219)( 72,218)
( 73,224)( 74,223)( 75,222)( 76,221)( 77,220)( 78,212)( 79,211)( 80,217)
( 81,216)( 82,215)( 83,214)( 84,213)( 85,240)( 86,239)( 87,245)( 88,244)
( 89,243)( 90,242)( 91,241)( 92,233)( 93,232)( 94,238)( 95,237)( 96,236)
( 97,235)( 98,234)( 99,226)(100,225)(101,231)(102,230)(103,229)(104,228)
(105,227)(106,254)(107,253)(108,259)(109,258)(110,257)(111,256)(112,255)
(113,247)(114,246)(115,252)(116,251)(117,250)(118,249)(119,248)(120,275)
(121,274)(122,280)(123,279)(124,278)(125,277)(126,276)(127,268)(128,267)
(129,273)(130,272)(131,271)(132,270)(133,269)(134,261)(135,260)(136,266)
(137,265)(138,264)(139,263)(140,262);;
s2 := (141,211)(142,212)(143,213)(144,214)(145,215)(146,216)(147,217)(148,218)
(149,219)(150,220)(151,221)(152,222)(153,223)(154,224)(155,225)(156,226)
(157,227)(158,228)(159,229)(160,230)(161,231)(162,232)(163,233)(164,234)
(165,235)(166,236)(167,237)(168,238)(169,239)(170,240)(171,241)(172,242)
(173,243)(174,244)(175,245)(176,246)(177,247)(178,248)(179,249)(180,250)
(181,251)(182,252)(183,253)(184,254)(185,255)(186,256)(187,257)(188,258)
(189,259)(190,260)(191,261)(192,262)(193,263)(194,264)(195,265)(196,266)
(197,267)(198,268)(199,269)(200,270)(201,271)(202,272)(203,273)(204,274)
(205,275)(206,276)(207,277)(208,278)(209,279)(210,280);;
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*s2*s0*s2, s0*s1*s2*s1*s0*s1*s2*s1, 
s1*s2*s1*s2*s1*s2*s1*s2, s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*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)( 72, 77)( 73, 76)( 74, 75)( 78, 99)( 79,105)
( 80,104)( 81,103)( 82,102)( 83,101)( 84,100)( 85, 92)( 86, 98)( 87, 97)
( 88, 96)( 89, 95)( 90, 94)( 91, 93)(107,112)(108,111)(109,110)(113,134)
(114,140)(115,139)(116,138)(117,137)(118,136)(119,135)(120,127)(121,133)
(122,132)(123,131)(124,130)(125,129)(126,128)(141,176)(142,182)(143,181)
(144,180)(145,179)(146,178)(147,177)(148,204)(149,210)(150,209)(151,208)
(152,207)(153,206)(154,205)(155,197)(156,203)(157,202)(158,201)(159,200)
(160,199)(161,198)(162,190)(163,196)(164,195)(165,194)(166,193)(167,192)
(168,191)(169,183)(170,189)(171,188)(172,187)(173,186)(174,185)(175,184)
(211,246)(212,252)(213,251)(214,250)(215,249)(216,248)(217,247)(218,274)
(219,280)(220,279)(221,278)(222,277)(223,276)(224,275)(225,267)(226,273)
(227,272)(228,271)(229,270)(230,269)(231,268)(232,260)(233,266)(234,265)
(235,264)(236,263)(237,262)(238,261)(239,253)(240,259)(241,258)(242,257)
(243,256)(244,255)(245,254);
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)( 71,219)
( 72,218)( 73,224)( 74,223)( 75,222)( 76,221)( 77,220)( 78,212)( 79,211)
( 80,217)( 81,216)( 82,215)( 83,214)( 84,213)( 85,240)( 86,239)( 87,245)
( 88,244)( 89,243)( 90,242)( 91,241)( 92,233)( 93,232)( 94,238)( 95,237)
( 96,236)( 97,235)( 98,234)( 99,226)(100,225)(101,231)(102,230)(103,229)
(104,228)(105,227)(106,254)(107,253)(108,259)(109,258)(110,257)(111,256)
(112,255)(113,247)(114,246)(115,252)(116,251)(117,250)(118,249)(119,248)
(120,275)(121,274)(122,280)(123,279)(124,278)(125,277)(126,276)(127,268)
(128,267)(129,273)(130,272)(131,271)(132,270)(133,269)(134,261)(135,260)
(136,266)(137,265)(138,264)(139,263)(140,262);
s2 := Sym(280)!(141,211)(142,212)(143,213)(144,214)(145,215)(146,216)(147,217)
(148,218)(149,219)(150,220)(151,221)(152,222)(153,223)(154,224)(155,225)
(156,226)(157,227)(158,228)(159,229)(160,230)(161,231)(162,232)(163,233)
(164,234)(165,235)(166,236)(167,237)(168,238)(169,239)(170,240)(171,241)
(172,242)(173,243)(174,244)(175,245)(176,246)(177,247)(178,248)(179,249)
(180,250)(181,251)(182,252)(183,253)(184,254)(185,255)(186,256)(187,257)
(188,258)(189,259)(190,260)(191,261)(192,262)(193,263)(194,264)(195,265)
(196,266)(197,267)(198,268)(199,269)(200,270)(201,271)(202,272)(203,273)
(204,274)(205,275)(206,276)(207,277)(208,278)(209,279)(210,280);
poly := sub<Sym(280)|s0,s1,s2>;

Finitely Presented Group Representation (Magma) :

poly<s0,s1,s2> := Group< s0,s1,s2 | s0*s0, s1*s1, s2*s2, 
s0*s2*s0*s2, s0*s1*s2*s1*s0*s1*s2*s1, 
s1*s2*s1*s2*s1*s2*s1*s2, s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*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