Polytope of Type {70,8}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {70,8}*1120
Also Known As : {70,8|2}. if this polytope has another name.
Group : SmallGroup(1120,846)
Rank : 3
Schlafli Type : {70,8}
Number of vertices, edges, etc : 70, 280, 8
Order of s₀s₁s₂ : 280
Order of s₀s₁s₂s₁ : 2
Special Properties :
   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 : {70,4}*560
   4-fold quotients : {70,2}*280
   5-fold quotients : {14,8}*224
   7-fold quotients : {10,8}*160
   8-fold quotients : {35,2}*140
   10-fold quotients : {14,4}*112
   14-fold quotients : {10,4}*80
   20-fold quotients : {14,2}*56
   28-fold quotients : {10,2}*40
   35-fold quotients : {2,8}*32
   40-fold quotients : {7,2}*28
   56-fold quotients : {5,2}*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 := (  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)(142,147)(143,146)(144,145)(148,169)
(149,175)(150,174)(151,173)(152,172)(153,171)(154,170)(155,162)(156,168)
(157,167)(158,166)(159,165)(160,164)(161,163)(177,182)(178,181)(179,180)
(183,204)(184,210)(185,209)(186,208)(187,207)(188,206)(189,205)(190,197)
(191,203)(192,202)(193,201)(194,200)(195,199)(196,198)(212,217)(213,216)
(214,215)(218,239)(219,245)(220,244)(221,243)(222,242)(223,241)(224,240)
(225,232)(226,238)(227,237)(228,236)(229,235)(230,234)(231,233)(247,252)
(248,251)(249,250)(253,274)(254,280)(255,279)(256,278)(257,277)(258,276)
(259,275)(260,267)(261,273)(262,272)(263,271)(264,270)(265,269)(266,268);;
s1 := (  1,  9)(  2,  8)(  3, 14)(  4, 13)(  5, 12)(  6, 11)(  7, 10)( 15, 30)
( 16, 29)( 17, 35)( 18, 34)( 19, 33)( 20, 32)( 21, 31)( 22, 23)( 24, 28)
( 25, 27)( 36, 44)( 37, 43)( 38, 49)( 39, 48)( 40, 47)( 41, 46)( 42, 45)
( 50, 65)( 51, 64)( 52, 70)( 53, 69)( 54, 68)( 55, 67)( 56, 66)( 57, 58)
( 59, 63)( 60, 62)( 71,114)( 72,113)( 73,119)( 74,118)( 75,117)( 76,116)
( 77,115)( 78,107)( 79,106)( 80,112)( 81,111)( 82,110)( 83,109)( 84,108)
( 85,135)( 86,134)( 87,140)( 88,139)( 89,138)( 90,137)( 91,136)( 92,128)
( 93,127)( 94,133)( 95,132)( 96,131)( 97,130)( 98,129)( 99,121)(100,120)
(101,126)(102,125)(103,124)(104,123)(105,122)(141,219)(142,218)(143,224)
(144,223)(145,222)(146,221)(147,220)(148,212)(149,211)(150,217)(151,216)
(152,215)(153,214)(154,213)(155,240)(156,239)(157,245)(158,244)(159,243)
(160,242)(161,241)(162,233)(163,232)(164,238)(165,237)(166,236)(167,235)
(168,234)(169,226)(170,225)(171,231)(172,230)(173,229)(174,228)(175,227)
(176,254)(177,253)(178,259)(179,258)(180,257)(181,256)(182,255)(183,247)
(184,246)(185,252)(186,251)(187,250)(188,249)(189,248)(190,275)(191,274)
(192,280)(193,279)(194,278)(195,277)(196,276)(197,268)(198,267)(199,273)
(200,272)(201,271)(202,270)(203,269)(204,261)(205,260)(206,266)(207,265)
(208,264)(209,263)(210,262);;
s2 := (  1,141)(  2,142)(  3,143)(  4,144)(  5,145)(  6,146)(  7,147)(  8,148)
(  9,149)( 10,150)( 11,151)( 12,152)( 13,153)( 14,154)( 15,155)( 16,156)
( 17,157)( 18,158)( 19,159)( 20,160)( 21,161)( 22,162)( 23,163)( 24,164)
( 25,165)( 26,166)( 27,167)( 28,168)( 29,169)( 30,170)( 31,171)( 32,172)
( 33,173)( 34,174)( 35,175)( 36,176)( 37,177)( 38,178)( 39,179)( 40,180)
( 41,181)( 42,182)( 43,183)( 44,184)( 45,185)( 46,186)( 47,187)( 48,188)
( 49,189)( 50,190)( 51,191)( 52,192)( 53,193)( 54,194)( 55,195)( 56,196)
( 57,197)( 58,198)( 59,199)( 60,200)( 61,201)( 62,202)( 63,203)( 64,204)
( 65,205)( 66,206)( 67,207)( 68,208)( 69,209)( 70,210)( 71,246)( 72,247)
( 73,248)( 74,249)( 75,250)( 76,251)( 77,252)( 78,253)( 79,254)( 80,255)
( 81,256)( 82,257)( 83,258)( 84,259)( 85,260)( 86,261)( 87,262)( 88,263)
( 89,264)( 90,265)( 91,266)( 92,267)( 93,268)( 94,269)( 95,270)( 96,271)
( 97,272)( 98,273)( 99,274)(100,275)(101,276)(102,277)(103,278)(104,279)
(105,280)(106,211)(107,212)(108,213)(109,214)(110,215)(111,216)(112,217)
(113,218)(114,219)(115,220)(116,221)(117,222)(118,223)(119,224)(120,225)
(121,226)(122,227)(123,228)(124,229)(125,230)(126,231)(127,232)(128,233)
(129,234)(130,235)(131,236)(132,237)(133,238)(134,239)(135,240)(136,241)
(137,242)(138,243)(139,244)(140,245);;
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*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 ];;
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)(142,147)(143,146)(144,145)
(148,169)(149,175)(150,174)(151,173)(152,172)(153,171)(154,170)(155,162)
(156,168)(157,167)(158,166)(159,165)(160,164)(161,163)(177,182)(178,181)
(179,180)(183,204)(184,210)(185,209)(186,208)(187,207)(188,206)(189,205)
(190,197)(191,203)(192,202)(193,201)(194,200)(195,199)(196,198)(212,217)
(213,216)(214,215)(218,239)(219,245)(220,244)(221,243)(222,242)(223,241)
(224,240)(225,232)(226,238)(227,237)(228,236)(229,235)(230,234)(231,233)
(247,252)(248,251)(249,250)(253,274)(254,280)(255,279)(256,278)(257,277)
(258,276)(259,275)(260,267)(261,273)(262,272)(263,271)(264,270)(265,269)
(266,268);
s1 := Sym(280)!(  1,  9)(  2,  8)(  3, 14)(  4, 13)(  5, 12)(  6, 11)(  7, 10)
( 15, 30)( 16, 29)( 17, 35)( 18, 34)( 19, 33)( 20, 32)( 21, 31)( 22, 23)
( 24, 28)( 25, 27)( 36, 44)( 37, 43)( 38, 49)( 39, 48)( 40, 47)( 41, 46)
( 42, 45)( 50, 65)( 51, 64)( 52, 70)( 53, 69)( 54, 68)( 55, 67)( 56, 66)
( 57, 58)( 59, 63)( 60, 62)( 71,114)( 72,113)( 73,119)( 74,118)( 75,117)
( 76,116)( 77,115)( 78,107)( 79,106)( 80,112)( 81,111)( 82,110)( 83,109)
( 84,108)( 85,135)( 86,134)( 87,140)( 88,139)( 89,138)( 90,137)( 91,136)
( 92,128)( 93,127)( 94,133)( 95,132)( 96,131)( 97,130)( 98,129)( 99,121)
(100,120)(101,126)(102,125)(103,124)(104,123)(105,122)(141,219)(142,218)
(143,224)(144,223)(145,222)(146,221)(147,220)(148,212)(149,211)(150,217)
(151,216)(152,215)(153,214)(154,213)(155,240)(156,239)(157,245)(158,244)
(159,243)(160,242)(161,241)(162,233)(163,232)(164,238)(165,237)(166,236)
(167,235)(168,234)(169,226)(170,225)(171,231)(172,230)(173,229)(174,228)
(175,227)(176,254)(177,253)(178,259)(179,258)(180,257)(181,256)(182,255)
(183,247)(184,246)(185,252)(186,251)(187,250)(188,249)(189,248)(190,275)
(191,274)(192,280)(193,279)(194,278)(195,277)(196,276)(197,268)(198,267)
(199,273)(200,272)(201,271)(202,270)(203,269)(204,261)(205,260)(206,266)
(207,265)(208,264)(209,263)(210,262);
s2 := Sym(280)!(  1,141)(  2,142)(  3,143)(  4,144)(  5,145)(  6,146)(  7,147)
(  8,148)(  9,149)( 10,150)( 11,151)( 12,152)( 13,153)( 14,154)( 15,155)
( 16,156)( 17,157)( 18,158)( 19,159)( 20,160)( 21,161)( 22,162)( 23,163)
( 24,164)( 25,165)( 26,166)( 27,167)( 28,168)( 29,169)( 30,170)( 31,171)
( 32,172)( 33,173)( 34,174)( 35,175)( 36,176)( 37,177)( 38,178)( 39,179)
( 40,180)( 41,181)( 42,182)( 43,183)( 44,184)( 45,185)( 46,186)( 47,187)
( 48,188)( 49,189)( 50,190)( 51,191)( 52,192)( 53,193)( 54,194)( 55,195)
( 56,196)( 57,197)( 58,198)( 59,199)( 60,200)( 61,201)( 62,202)( 63,203)
( 64,204)( 65,205)( 66,206)( 67,207)( 68,208)( 69,209)( 70,210)( 71,246)
( 72,247)( 73,248)( 74,249)( 75,250)( 76,251)( 77,252)( 78,253)( 79,254)
( 80,255)( 81,256)( 82,257)( 83,258)( 84,259)( 85,260)( 86,261)( 87,262)
( 88,263)( 89,264)( 90,265)( 91,266)( 92,267)( 93,268)( 94,269)( 95,270)
( 96,271)( 97,272)( 98,273)( 99,274)(100,275)(101,276)(102,277)(103,278)
(104,279)(105,280)(106,211)(107,212)(108,213)(109,214)(110,215)(111,216)
(112,217)(113,218)(114,219)(115,220)(116,221)(117,222)(118,223)(119,224)
(120,225)(121,226)(122,227)(123,228)(124,229)(125,230)(126,231)(127,232)
(128,233)(129,234)(130,235)(131,236)(132,237)(133,238)(134,239)(135,240)
(136,241)(137,242)(138,243)(139,244)(140,245);
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*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 >;

References : None.
to this polytope