Polytope of Type {70,10}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {70,10}*1400c
if this polytope has a 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 : 10
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) :
   2-fold quotients : {35,10}*700
   5-fold quotients : {70,2}*280
   7-fold quotients : {10,10}*200c
   10-fold quotients : {35,2}*140
   14-fold quotients : {5,10}*100
   25-fold quotients : {14,2}*56
   35-fold quotients : {10,2}*40
   50-fold quotients : {7,2}*28
   70-fold quotients : {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)( 36,141)( 37,147)( 38,146)( 39,145)( 40,144)( 41,143)( 42,142)
( 43,169)( 44,175)( 45,174)( 46,173)( 47,172)( 48,171)( 49,170)( 50,162)
( 51,168)( 52,167)( 53,166)( 54,165)( 55,164)( 56,163)( 57,155)( 58,161)
( 59,160)( 60,159)( 61,158)( 62,157)( 63,156)( 64,148)( 65,154)( 66,153)
( 67,152)( 68,151)( 69,150)( 70,149)( 71,106)( 72,112)( 73,111)( 74,110)
( 75,109)( 76,108)( 77,107)( 78,134)( 79,140)( 80,139)( 81,138)( 82,137)
( 83,136)( 84,135)( 85,127)( 86,133)( 87,132)( 88,131)( 89,130)( 90,129)
( 91,128)( 92,120)( 93,126)( 94,125)( 95,124)( 96,123)( 97,122)( 98,121)
( 99,113)(100,119)(101,118)(102,117)(103,116)(104,115)(105,114)(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)
(211,316)(212,322)(213,321)(214,320)(215,319)(216,318)(217,317)(218,344)
(219,350)(220,349)(221,348)(222,347)(223,346)(224,345)(225,337)(226,343)
(227,342)(228,341)(229,340)(230,339)(231,338)(232,330)(233,336)(234,335)
(235,334)(236,333)(237,332)(238,331)(239,323)(240,329)(241,328)(242,327)
(243,326)(244,325)(245,324)(246,281)(247,287)(248,286)(249,285)(250,284)
(251,283)(252,282)(253,309)(254,315)(255,314)(256,313)(257,312)(258,311)
(259,310)(260,302)(261,308)(262,307)(263,306)(264,305)(265,304)(266,303)
(267,295)(268,301)(269,300)(270,299)(271,298)(272,297)(273,296)(274,288)
(275,294)(276,293)(277,292)(278,291)(279,290)(280,289);;
s1 := (  1,219)(  2,218)(  3,224)(  4,223)(  5,222)(  6,221)(  7,220)(  8,212)
(  9,211)( 10,217)( 11,216)( 12,215)( 13,214)( 14,213)( 15,240)( 16,239)
( 17,245)( 18,244)( 19,243)( 20,242)( 21,241)( 22,233)( 23,232)( 24,238)
( 25,237)( 26,236)( 27,235)( 28,234)( 29,226)( 30,225)( 31,231)( 32,230)
( 33,229)( 34,228)( 35,227)( 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)( 71,324)( 72,323)
( 73,329)( 74,328)( 75,327)( 76,326)( 77,325)( 78,317)( 79,316)( 80,322)
( 81,321)( 82,320)( 83,319)( 84,318)( 85,345)( 86,344)( 87,350)( 88,349)
( 89,348)( 90,347)( 91,346)( 92,338)( 93,337)( 94,343)( 95,342)( 96,341)
( 97,340)( 98,339)( 99,331)(100,330)(101,336)(102,335)(103,334)(104,333)
(105,332)(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)(141,254)(142,253)(143,259)(144,258)
(145,257)(146,256)(147,255)(148,247)(149,246)(150,252)(151,251)(152,250)
(153,249)(154,248)(155,275)(156,274)(157,280)(158,279)(159,278)(160,277)
(161,276)(162,268)(163,267)(164,273)(165,272)(166,271)(167,270)(168,269)
(169,261)(170,260)(171,266)(172,265)(173,264)(174,263)(175,262);;
s2 := ( 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);;
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*s2*s1*s2*s0*s1*s2*s1, 
s0*s1*s2*s1*s0*s1*s0*s1*s0*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*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*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)( 36,141)( 37,147)( 38,146)( 39,145)( 40,144)( 41,143)
( 42,142)( 43,169)( 44,175)( 45,174)( 46,173)( 47,172)( 48,171)( 49,170)
( 50,162)( 51,168)( 52,167)( 53,166)( 54,165)( 55,164)( 56,163)( 57,155)
( 58,161)( 59,160)( 60,159)( 61,158)( 62,157)( 63,156)( 64,148)( 65,154)
( 66,153)( 67,152)( 68,151)( 69,150)( 70,149)( 71,106)( 72,112)( 73,111)
( 74,110)( 75,109)( 76,108)( 77,107)( 78,134)( 79,140)( 80,139)( 81,138)
( 82,137)( 83,136)( 84,135)( 85,127)( 86,133)( 87,132)( 88,131)( 89,130)
( 90,129)( 91,128)( 92,120)( 93,126)( 94,125)( 95,124)( 96,123)( 97,122)
( 98,121)( 99,113)(100,119)(101,118)(102,117)(103,116)(104,115)(105,114)
(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)(211,316)(212,322)(213,321)(214,320)(215,319)(216,318)(217,317)
(218,344)(219,350)(220,349)(221,348)(222,347)(223,346)(224,345)(225,337)
(226,343)(227,342)(228,341)(229,340)(230,339)(231,338)(232,330)(233,336)
(234,335)(235,334)(236,333)(237,332)(238,331)(239,323)(240,329)(241,328)
(242,327)(243,326)(244,325)(245,324)(246,281)(247,287)(248,286)(249,285)
(250,284)(251,283)(252,282)(253,309)(254,315)(255,314)(256,313)(257,312)
(258,311)(259,310)(260,302)(261,308)(262,307)(263,306)(264,305)(265,304)
(266,303)(267,295)(268,301)(269,300)(270,299)(271,298)(272,297)(273,296)
(274,288)(275,294)(276,293)(277,292)(278,291)(279,290)(280,289);
s1 := Sym(350)!(  1,219)(  2,218)(  3,224)(  4,223)(  5,222)(  6,221)(  7,220)
(  8,212)(  9,211)( 10,217)( 11,216)( 12,215)( 13,214)( 14,213)( 15,240)
( 16,239)( 17,245)( 18,244)( 19,243)( 20,242)( 21,241)( 22,233)( 23,232)
( 24,238)( 25,237)( 26,236)( 27,235)( 28,234)( 29,226)( 30,225)( 31,231)
( 32,230)( 33,229)( 34,228)( 35,227)( 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)( 71,324)
( 72,323)( 73,329)( 74,328)( 75,327)( 76,326)( 77,325)( 78,317)( 79,316)
( 80,322)( 81,321)( 82,320)( 83,319)( 84,318)( 85,345)( 86,344)( 87,350)
( 88,349)( 89,348)( 90,347)( 91,346)( 92,338)( 93,337)( 94,343)( 95,342)
( 96,341)( 97,340)( 98,339)( 99,331)(100,330)(101,336)(102,335)(103,334)
(104,333)(105,332)(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)(141,254)(142,253)(143,259)
(144,258)(145,257)(146,256)(147,255)(148,247)(149,246)(150,252)(151,251)
(152,250)(153,249)(154,248)(155,275)(156,274)(157,280)(158,279)(159,278)
(160,277)(161,276)(162,268)(163,267)(164,273)(165,272)(166,271)(167,270)
(168,269)(169,261)(170,260)(171,266)(172,265)(173,264)(174,263)(175,262);
s2 := 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);
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*s2*s1*s2*s0*s1*s2*s1, 
s0*s1*s2*s1*s0*s1*s0*s1*s0*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*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*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