Polytope of Type {10,70}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {10,70}*1400b
Also Known As : {10,70|2}. if this polytope has another 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 : 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) :
5-fold quotients : {10,14}*280, {2,70}*280
7-fold quotients : {10,10}*200a
10-fold quotients : {2,35}*140
25-fold quotients : {2,14}*56
35-fold quotients : {2,10}*40, {10,2}*40
50-fold quotients : {2,7}*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 := ( 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)( 36,219)( 37,218)( 38,224)( 39,223)( 40,222)
( 41,221)( 42,220)( 43,212)( 44,211)( 45,217)( 46,216)( 47,215)( 48,214)
( 49,213)( 50,240)( 51,239)( 52,245)( 53,244)( 54,243)( 55,242)( 56,241)
( 57,233)( 58,232)( 59,238)( 60,237)( 61,236)( 62,235)( 63,234)( 64,226)
( 65,225)( 66,231)( 67,230)( 68,229)( 69,228)( 70,227)( 71,254)( 72,253)
( 73,259)( 74,258)( 75,257)( 76,256)( 77,255)( 78,247)( 79,246)( 80,252)
( 81,251)( 82,250)( 83,249)( 84,248)( 85,275)( 86,274)( 87,280)( 88,279)
( 89,278)( 90,277)( 91,276)( 92,268)( 93,267)( 94,273)( 95,272)( 96,271)
( 97,270)( 98,269)( 99,261)(100,260)(101,266)(102,265)(103,264)(104,263)
(105,262)(106,289)(107,288)(108,294)(109,293)(110,292)(111,291)(112,290)
(113,282)(114,281)(115,287)(116,286)(117,285)(118,284)(119,283)(120,310)
(121,309)(122,315)(123,314)(124,313)(125,312)(126,311)(127,303)(128,302)
(129,308)(130,307)(131,306)(132,305)(133,304)(134,296)(135,295)(136,301)
(137,300)(138,299)(139,298)(140,297)(141,324)(142,323)(143,329)(144,328)
(145,327)(146,326)(147,325)(148,317)(149,316)(150,322)(151,321)(152,320)
(153,319)(154,318)(155,345)(156,344)(157,350)(158,349)(159,348)(160,347)
(161,346)(162,338)(163,337)(164,343)(165,342)(166,341)(167,340)(168,339)
(169,331)(170,330)(171,336)(172,335)(173,334)(174,333)(175,332);;
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,
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)( 36,219)( 37,218)( 38,224)( 39,223)
( 40,222)( 41,221)( 42,220)( 43,212)( 44,211)( 45,217)( 46,216)( 47,215)
( 48,214)( 49,213)( 50,240)( 51,239)( 52,245)( 53,244)( 54,243)( 55,242)
( 56,241)( 57,233)( 58,232)( 59,238)( 60,237)( 61,236)( 62,235)( 63,234)
( 64,226)( 65,225)( 66,231)( 67,230)( 68,229)( 69,228)( 70,227)( 71,254)
( 72,253)( 73,259)( 74,258)( 75,257)( 76,256)( 77,255)( 78,247)( 79,246)
( 80,252)( 81,251)( 82,250)( 83,249)( 84,248)( 85,275)( 86,274)( 87,280)
( 88,279)( 89,278)( 90,277)( 91,276)( 92,268)( 93,267)( 94,273)( 95,272)
( 96,271)( 97,270)( 98,269)( 99,261)(100,260)(101,266)(102,265)(103,264)
(104,263)(105,262)(106,289)(107,288)(108,294)(109,293)(110,292)(111,291)
(112,290)(113,282)(114,281)(115,287)(116,286)(117,285)(118,284)(119,283)
(120,310)(121,309)(122,315)(123,314)(124,313)(125,312)(126,311)(127,303)
(128,302)(129,308)(130,307)(131,306)(132,305)(133,304)(134,296)(135,295)
(136,301)(137,300)(138,299)(139,298)(140,297)(141,324)(142,323)(143,329)
(144,328)(145,327)(146,326)(147,325)(148,317)(149,316)(150,322)(151,321)
(152,320)(153,319)(154,318)(155,345)(156,344)(157,350)(158,349)(159,348)
(160,347)(161,346)(162,338)(163,337)(164,343)(165,342)(166,341)(167,340)
(168,339)(169,331)(170,330)(171,336)(172,335)(173,334)(174,333)(175,332);
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,
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