Polytope of Type {70,10}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {70,10}*1400b
Also Known As : {70,10|2}. if this polytope has another name.
Group : SmallGroup(1400,146)
Rank : 3
Schlafli Type : {70,10}
Number of vertices, edges, etc : 70, 350, 10
Order of s₀s₁s₂ : 70
Order of s₀s₁s₂s₁ : 2
Special Properties :
   Compact Hyperbolic Quotient
   Locally Spherical
   Orientable
   Flat
Related Polytopes :
   Facet
   Vertex Figure
   Dual
   Petrial
Facet Of :
   None in this Atlas
Vertex Figure Of :
   None in this Atlas
Quotients (Maximal Quotients in Boldface) :
   5-fold quotients : {14,10}*280, {70,2}*280
   7-fold quotients : {10,10}*200a
   10-fold quotients : {35,2}*140
   25-fold quotients : {14,2}*56
   35-fold quotients : {2,10}*40, {10,2}*40
   50-fold quotients : {7,2}*28
   70-fold quotients : {2,5}*20, {5,2}*20
   175-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)
(282,287)(283,286)(284,285)(288,309)(289,315)(290,314)(291,313)(292,312)
(293,311)(294,310)(295,302)(296,308)(297,307)(298,306)(299,305)(300,304)
(301,303)(317,322)(318,321)(319,320)(323,344)(324,350)(325,349)(326,348)
(327,347)(328,346)(329,345)(330,337)(331,343)(332,342)(333,341)(334,340)
(335,339)(336,338);;
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)( 36,149)( 37,148)( 38,154)( 39,153)( 40,152)( 41,151)( 42,150)
( 43,142)( 44,141)( 45,147)( 46,146)( 47,145)( 48,144)( 49,143)( 50,170)
( 51,169)( 52,175)( 53,174)( 54,173)( 55,172)( 56,171)( 57,163)( 58,162)
( 59,168)( 60,167)( 61,166)( 62,165)( 63,164)( 64,156)( 65,155)( 66,161)
( 67,160)( 68,159)( 69,158)( 70,157)( 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)(176,184)
(177,183)(178,189)(179,188)(180,187)(181,186)(182,185)(190,205)(191,204)
(192,210)(193,209)(194,208)(195,207)(196,206)(197,198)(199,203)(200,202)
(211,324)(212,323)(213,329)(214,328)(215,327)(216,326)(217,325)(218,317)
(219,316)(220,322)(221,321)(222,320)(223,319)(224,318)(225,345)(226,344)
(227,350)(228,349)(229,348)(230,347)(231,346)(232,338)(233,337)(234,343)
(235,342)(236,341)(237,340)(238,339)(239,331)(240,330)(241,336)(242,335)
(243,334)(244,333)(245,332)(246,289)(247,288)(248,294)(249,293)(250,292)
(251,291)(252,290)(253,282)(254,281)(255,287)(256,286)(257,285)(258,284)
(259,283)(260,310)(261,309)(262,315)(263,314)(264,313)(265,312)(266,311)
(267,303)(268,302)(269,308)(270,307)(271,306)(272,305)(273,304)(274,296)
(275,295)(276,301)(277,300)(278,299)(279,298)(280,297);;
s2 := (  1,211)(  2,212)(  3,213)(  4,214)(  5,215)(  6,216)(  7,217)(  8,218)
(  9,219)( 10,220)( 11,221)( 12,222)( 13,223)( 14,224)( 15,225)( 16,226)
( 17,227)( 18,228)( 19,229)( 20,230)( 21,231)( 22,232)( 23,233)( 24,234)
( 25,235)( 26,236)( 27,237)( 28,238)( 29,239)( 30,240)( 31,241)( 32,242)
( 33,243)( 34,244)( 35,245)( 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)( 71,316)( 72,317)
( 73,318)( 74,319)( 75,320)( 76,321)( 77,322)( 78,323)( 79,324)( 80,325)
( 81,326)( 82,327)( 83,328)( 84,329)( 85,330)( 86,331)( 87,332)( 88,333)
( 89,334)( 90,335)( 91,336)( 92,337)( 93,338)( 94,339)( 95,340)( 96,341)
( 97,342)( 98,343)( 99,344)(100,345)(101,346)(102,347)(103,348)(104,349)
(105,350)(106,281)(107,282)(108,283)(109,284)(110,285)(111,286)(112,287)
(113,288)(114,289)(115,290)(116,291)(117,292)(118,293)(119,294)(120,295)
(121,296)(122,297)(123,298)(124,299)(125,300)(126,301)(127,302)(128,303)
(129,304)(130,305)(131,306)(132,307)(133,308)(134,309)(135,310)(136,311)
(137,312)(138,313)(139,314)(140,315)(141,246)(142,247)(143,248)(144,249)
(145,250)(146,251)(147,252)(148,253)(149,254)(150,255)(151,256)(152,257)
(153,258)(154,259)(155,260)(156,261)(157,262)(158,263)(159,264)(160,265)
(161,266)(162,267)(163,268)(164,269)(165,270)(166,271)(167,272)(168,273)
(169,274)(170,275)(171,276)(172,277)(173,278)(174,279)(175,280);;
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*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(350)!(  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)(282,287)(283,286)(284,285)(288,309)(289,315)(290,314)(291,313)
(292,312)(293,311)(294,310)(295,302)(296,308)(297,307)(298,306)(299,305)
(300,304)(301,303)(317,322)(318,321)(319,320)(323,344)(324,350)(325,349)
(326,348)(327,347)(328,346)(329,345)(330,337)(331,343)(332,342)(333,341)
(334,340)(335,339)(336,338);
s1 := Sym(350)!(  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)( 36,149)( 37,148)( 38,154)( 39,153)( 40,152)( 41,151)
( 42,150)( 43,142)( 44,141)( 45,147)( 46,146)( 47,145)( 48,144)( 49,143)
( 50,170)( 51,169)( 52,175)( 53,174)( 54,173)( 55,172)( 56,171)( 57,163)
( 58,162)( 59,168)( 60,167)( 61,166)( 62,165)( 63,164)( 64,156)( 65,155)
( 66,161)( 67,160)( 68,159)( 69,158)( 70,157)( 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)
(176,184)(177,183)(178,189)(179,188)(180,187)(181,186)(182,185)(190,205)
(191,204)(192,210)(193,209)(194,208)(195,207)(196,206)(197,198)(199,203)
(200,202)(211,324)(212,323)(213,329)(214,328)(215,327)(216,326)(217,325)
(218,317)(219,316)(220,322)(221,321)(222,320)(223,319)(224,318)(225,345)
(226,344)(227,350)(228,349)(229,348)(230,347)(231,346)(232,338)(233,337)
(234,343)(235,342)(236,341)(237,340)(238,339)(239,331)(240,330)(241,336)
(242,335)(243,334)(244,333)(245,332)(246,289)(247,288)(248,294)(249,293)
(250,292)(251,291)(252,290)(253,282)(254,281)(255,287)(256,286)(257,285)
(258,284)(259,283)(260,310)(261,309)(262,315)(263,314)(264,313)(265,312)
(266,311)(267,303)(268,302)(269,308)(270,307)(271,306)(272,305)(273,304)
(274,296)(275,295)(276,301)(277,300)(278,299)(279,298)(280,297);
s2 := Sym(350)!(  1,211)(  2,212)(  3,213)(  4,214)(  5,215)(  6,216)(  7,217)
(  8,218)(  9,219)( 10,220)( 11,221)( 12,222)( 13,223)( 14,224)( 15,225)
( 16,226)( 17,227)( 18,228)( 19,229)( 20,230)( 21,231)( 22,232)( 23,233)
( 24,234)( 25,235)( 26,236)( 27,237)( 28,238)( 29,239)( 30,240)( 31,241)
( 32,242)( 33,243)( 34,244)( 35,245)( 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)( 71,316)
( 72,317)( 73,318)( 74,319)( 75,320)( 76,321)( 77,322)( 78,323)( 79,324)
( 80,325)( 81,326)( 82,327)( 83,328)( 84,329)( 85,330)( 86,331)( 87,332)
( 88,333)( 89,334)( 90,335)( 91,336)( 92,337)( 93,338)( 94,339)( 95,340)
( 96,341)( 97,342)( 98,343)( 99,344)(100,345)(101,346)(102,347)(103,348)
(104,349)(105,350)(106,281)(107,282)(108,283)(109,284)(110,285)(111,286)
(112,287)(113,288)(114,289)(115,290)(116,291)(117,292)(118,293)(119,294)
(120,295)(121,296)(122,297)(123,298)(124,299)(125,300)(126,301)(127,302)
(128,303)(129,304)(130,305)(131,306)(132,307)(133,308)(134,309)(135,310)
(136,311)(137,312)(138,313)(139,314)(140,315)(141,246)(142,247)(143,248)
(144,249)(145,250)(146,251)(147,252)(148,253)(149,254)(150,255)(151,256)
(152,257)(153,258)(154,259)(155,260)(156,261)(157,262)(158,263)(159,264)
(160,265)(161,266)(162,267)(163,268)(164,269)(165,270)(166,271)(167,272)
(168,273)(169,274)(170,275)(171,276)(172,277)(173,278)(174,279)(175,280);
poly := sub<Sym(350)|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*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