Polytope of Type {10,70}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {10,70}*1400c
if this polytope has a name.
Group : SmallGroup(1400,146)
Rank : 3
Schlafli Type : {10,70}
Number of vertices, edges, etc : 10, 350, 70
Order of s₀s₁s₂ : 70
Order of s₀s₁s₂s₁ : 10
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 : {10,35}*700
   5-fold quotients : {2,70}*280
   7-fold quotients : {10,10}*200b
   10-fold quotients : {2,35}*140
   14-fold quotients : {10,5}*100
   25-fold quotients : {2,14}*56
   35-fold quotients : {2,10}*40
   50-fold quotients : {2,7}*28
   70-fold quotients : {2,5}*20
   175-fold quotients : {2,2}*8
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :

s0 := ( 36,141)( 37,142)( 38,143)( 39,144)( 40,145)( 41,146)( 42,147)( 43,148)
( 44,149)( 45,150)( 46,151)( 47,152)( 48,153)( 49,154)( 50,155)( 51,156)
( 52,157)( 53,158)( 54,159)( 55,160)( 56,161)( 57,162)( 58,163)( 59,164)
( 60,165)( 61,166)( 62,167)( 63,168)( 64,169)( 65,170)( 66,171)( 67,172)
( 68,173)( 69,174)( 70,175)( 71,106)( 72,107)( 73,108)( 74,109)( 75,110)
( 76,111)( 77,112)( 78,113)( 79,114)( 80,115)( 81,116)( 82,117)( 83,118)
( 84,119)( 85,120)( 86,121)( 87,122)( 88,123)( 89,124)( 90,125)( 91,126)
( 92,127)( 93,128)( 94,129)( 95,130)( 96,131)( 97,132)( 98,133)( 99,134)
(100,135)(101,136)(102,137)(103,138)(104,139)(105,140)(211,316)(212,317)
(213,318)(214,319)(215,320)(216,321)(217,322)(218,323)(219,324)(220,325)
(221,326)(222,327)(223,328)(224,329)(225,330)(226,331)(227,332)(228,333)
(229,334)(230,335)(231,336)(232,337)(233,338)(234,339)(235,340)(236,341)
(237,342)(238,343)(239,344)(240,345)(241,346)(242,347)(243,348)(244,349)
(245,350)(246,281)(247,282)(248,283)(249,284)(250,285)(251,286)(252,287)
(253,288)(254,289)(255,290)(256,291)(257,292)(258,293)(259,294)(260,295)
(261,296)(262,297)(263,298)(264,299)(265,300)(266,301)(267,302)(268,303)
(269,304)(270,305)(271,306)(272,307)(273,308)(274,309)(275,310)(276,311)
(277,312)(278,313)(279,314)(280,315);;
s1 := (  1, 36)(  2, 42)(  3, 41)(  4, 40)(  5, 39)(  6, 38)(  7, 37)(  8, 64)
(  9, 70)( 10, 69)( 11, 68)( 12, 67)( 13, 66)( 14, 65)( 15, 57)( 16, 63)
( 17, 62)( 18, 61)( 19, 60)( 20, 59)( 21, 58)( 22, 50)( 23, 56)( 24, 55)
( 25, 54)( 26, 53)( 27, 52)( 28, 51)( 29, 43)( 30, 49)( 31, 48)( 32, 47)
( 33, 46)( 34, 45)( 35, 44)( 71,141)( 72,147)( 73,146)( 74,145)( 75,144)
( 76,143)( 77,142)( 78,169)( 79,175)( 80,174)( 81,173)( 82,172)( 83,171)
( 84,170)( 85,162)( 86,168)( 87,167)( 88,166)( 89,165)( 90,164)( 91,163)
( 92,155)( 93,161)( 94,160)( 95,159)( 96,158)( 97,157)( 98,156)( 99,148)
(100,154)(101,153)(102,152)(103,151)(104,150)(105,149)(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)(176,211)
(177,217)(178,216)(179,215)(180,214)(181,213)(182,212)(183,239)(184,245)
(185,244)(186,243)(187,242)(188,241)(189,240)(190,232)(191,238)(192,237)
(193,236)(194,235)(195,234)(196,233)(197,225)(198,231)(199,230)(200,229)
(201,228)(202,227)(203,226)(204,218)(205,224)(206,223)(207,222)(208,221)
(209,220)(210,219)(246,316)(247,322)(248,321)(249,320)(250,319)(251,318)
(252,317)(253,344)(254,350)(255,349)(256,348)(257,347)(258,346)(259,345)
(260,337)(261,343)(262,342)(263,341)(264,340)(265,339)(266,338)(267,330)
(268,336)(269,335)(270,334)(271,333)(272,332)(273,331)(274,323)(275,329)
(276,328)(277,327)(278,326)(279,325)(280,324)(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);;
s2 := (  1,184)(  2,183)(  3,189)(  4,188)(  5,187)(  6,186)(  7,185)(  8,177)
(  9,176)( 10,182)( 11,181)( 12,180)( 13,179)( 14,178)( 15,205)( 16,204)
( 17,210)( 18,209)( 19,208)( 20,207)( 21,206)( 22,198)( 23,197)( 24,203)
( 25,202)( 26,201)( 27,200)( 28,199)( 29,191)( 30,190)( 31,196)( 32,195)
( 33,194)( 34,193)( 35,192)( 36,324)( 37,323)( 38,329)( 39,328)( 40,327)
( 41,326)( 42,325)( 43,317)( 44,316)( 45,322)( 46,321)( 47,320)( 48,319)
( 49,318)( 50,345)( 51,344)( 52,350)( 53,349)( 54,348)( 55,347)( 56,346)
( 57,338)( 58,337)( 59,343)( 60,342)( 61,341)( 62,340)( 63,339)( 64,331)
( 65,330)( 66,336)( 67,335)( 68,334)( 69,333)( 70,332)( 71,289)( 72,288)
( 73,294)( 74,293)( 75,292)( 76,291)( 77,290)( 78,282)( 79,281)( 80,287)
( 81,286)( 82,285)( 83,284)( 84,283)( 85,310)( 86,309)( 87,315)( 88,314)
( 89,313)( 90,312)( 91,311)( 92,303)( 93,302)( 94,308)( 95,307)( 96,306)
( 97,305)( 98,304)( 99,296)(100,295)(101,301)(102,300)(103,299)(104,298)
(105,297)(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)(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);;
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, s2*s0*s1*s0*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, 
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*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(350)!( 36,141)( 37,142)( 38,143)( 39,144)( 40,145)( 41,146)( 42,147)
( 43,148)( 44,149)( 45,150)( 46,151)( 47,152)( 48,153)( 49,154)( 50,155)
( 51,156)( 52,157)( 53,158)( 54,159)( 55,160)( 56,161)( 57,162)( 58,163)
( 59,164)( 60,165)( 61,166)( 62,167)( 63,168)( 64,169)( 65,170)( 66,171)
( 67,172)( 68,173)( 69,174)( 70,175)( 71,106)( 72,107)( 73,108)( 74,109)
( 75,110)( 76,111)( 77,112)( 78,113)( 79,114)( 80,115)( 81,116)( 82,117)
( 83,118)( 84,119)( 85,120)( 86,121)( 87,122)( 88,123)( 89,124)( 90,125)
( 91,126)( 92,127)( 93,128)( 94,129)( 95,130)( 96,131)( 97,132)( 98,133)
( 99,134)(100,135)(101,136)(102,137)(103,138)(104,139)(105,140)(211,316)
(212,317)(213,318)(214,319)(215,320)(216,321)(217,322)(218,323)(219,324)
(220,325)(221,326)(222,327)(223,328)(224,329)(225,330)(226,331)(227,332)
(228,333)(229,334)(230,335)(231,336)(232,337)(233,338)(234,339)(235,340)
(236,341)(237,342)(238,343)(239,344)(240,345)(241,346)(242,347)(243,348)
(244,349)(245,350)(246,281)(247,282)(248,283)(249,284)(250,285)(251,286)
(252,287)(253,288)(254,289)(255,290)(256,291)(257,292)(258,293)(259,294)
(260,295)(261,296)(262,297)(263,298)(264,299)(265,300)(266,301)(267,302)
(268,303)(269,304)(270,305)(271,306)(272,307)(273,308)(274,309)(275,310)
(276,311)(277,312)(278,313)(279,314)(280,315);
s1 := Sym(350)!(  1, 36)(  2, 42)(  3, 41)(  4, 40)(  5, 39)(  6, 38)(  7, 37)
(  8, 64)(  9, 70)( 10, 69)( 11, 68)( 12, 67)( 13, 66)( 14, 65)( 15, 57)
( 16, 63)( 17, 62)( 18, 61)( 19, 60)( 20, 59)( 21, 58)( 22, 50)( 23, 56)
( 24, 55)( 25, 54)( 26, 53)( 27, 52)( 28, 51)( 29, 43)( 30, 49)( 31, 48)
( 32, 47)( 33, 46)( 34, 45)( 35, 44)( 71,141)( 72,147)( 73,146)( 74,145)
( 75,144)( 76,143)( 77,142)( 78,169)( 79,175)( 80,174)( 81,173)( 82,172)
( 83,171)( 84,170)( 85,162)( 86,168)( 87,167)( 88,166)( 89,165)( 90,164)
( 91,163)( 92,155)( 93,161)( 94,160)( 95,159)( 96,158)( 97,157)( 98,156)
( 99,148)(100,154)(101,153)(102,152)(103,151)(104,150)(105,149)(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)
(176,211)(177,217)(178,216)(179,215)(180,214)(181,213)(182,212)(183,239)
(184,245)(185,244)(186,243)(187,242)(188,241)(189,240)(190,232)(191,238)
(192,237)(193,236)(194,235)(195,234)(196,233)(197,225)(198,231)(199,230)
(200,229)(201,228)(202,227)(203,226)(204,218)(205,224)(206,223)(207,222)
(208,221)(209,220)(210,219)(246,316)(247,322)(248,321)(249,320)(250,319)
(251,318)(252,317)(253,344)(254,350)(255,349)(256,348)(257,347)(258,346)
(259,345)(260,337)(261,343)(262,342)(263,341)(264,340)(265,339)(266,338)
(267,330)(268,336)(269,335)(270,334)(271,333)(272,332)(273,331)(274,323)
(275,329)(276,328)(277,327)(278,326)(279,325)(280,324)(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);
s2 := Sym(350)!(  1,184)(  2,183)(  3,189)(  4,188)(  5,187)(  6,186)(  7,185)
(  8,177)(  9,176)( 10,182)( 11,181)( 12,180)( 13,179)( 14,178)( 15,205)
( 16,204)( 17,210)( 18,209)( 19,208)( 20,207)( 21,206)( 22,198)( 23,197)
( 24,203)( 25,202)( 26,201)( 27,200)( 28,199)( 29,191)( 30,190)( 31,196)
( 32,195)( 33,194)( 34,193)( 35,192)( 36,324)( 37,323)( 38,329)( 39,328)
( 40,327)( 41,326)( 42,325)( 43,317)( 44,316)( 45,322)( 46,321)( 47,320)
( 48,319)( 49,318)( 50,345)( 51,344)( 52,350)( 53,349)( 54,348)( 55,347)
( 56,346)( 57,338)( 58,337)( 59,343)( 60,342)( 61,341)( 62,340)( 63,339)
( 64,331)( 65,330)( 66,336)( 67,335)( 68,334)( 69,333)( 70,332)( 71,289)
( 72,288)( 73,294)( 74,293)( 75,292)( 76,291)( 77,290)( 78,282)( 79,281)
( 80,287)( 81,286)( 82,285)( 83,284)( 84,283)( 85,310)( 86,309)( 87,315)
( 88,314)( 89,313)( 90,312)( 91,311)( 92,303)( 93,302)( 94,308)( 95,307)
( 96,306)( 97,305)( 98,304)( 99,296)(100,295)(101,301)(102,300)(103,299)
(104,298)(105,297)(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)(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);
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, s2*s0*s1*s0*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, 
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2 >;

References : None.
to this polytope