Polytope of Type {50,14}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {50,14}*1400
Also Known As : {50,14|2}. if this polytope has another name.
Group : SmallGroup(1400,36)
Rank : 3
Schlafli Type : {50,14}
Number of vertices, edges, etc : 50, 350, 14
Order of s₀s₁s₂ : 350
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
   7-fold quotients : {50,2}*200
   14-fold quotients : {25,2}*100
   25-fold quotients : {2,14}*56
   35-fold quotients : {10,2}*40
   50-fold quotients : {2,7}*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,  5)(  3,  4)(  7, 10)(  8,  9)( 12, 15)( 13, 14)( 17, 20)( 18, 19)
( 22, 25)( 23, 24)( 27, 30)( 28, 29)( 32, 35)( 33, 34)( 36,142)( 37,141)
( 38,145)( 39,144)( 40,143)( 41,147)( 42,146)( 43,150)( 44,149)( 45,148)
( 46,152)( 47,151)( 48,155)( 49,154)( 50,153)( 51,157)( 52,156)( 53,160)
( 54,159)( 55,158)( 56,162)( 57,161)( 58,165)( 59,164)( 60,163)( 61,167)
( 62,166)( 63,170)( 64,169)( 65,168)( 66,172)( 67,171)( 68,175)( 69,174)
( 70,173)( 71,107)( 72,106)( 73,110)( 74,109)( 75,108)( 76,112)( 77,111)
( 78,115)( 79,114)( 80,113)( 81,117)( 82,116)( 83,120)( 84,119)( 85,118)
( 86,122)( 87,121)( 88,125)( 89,124)( 90,123)( 91,127)( 92,126)( 93,130)
( 94,129)( 95,128)( 96,132)( 97,131)( 98,135)( 99,134)(100,133)(101,137)
(102,136)(103,140)(104,139)(105,138)(177,180)(178,179)(182,185)(183,184)
(187,190)(188,189)(192,195)(193,194)(197,200)(198,199)(202,205)(203,204)
(207,210)(208,209)(211,317)(212,316)(213,320)(214,319)(215,318)(216,322)
(217,321)(218,325)(219,324)(220,323)(221,327)(222,326)(223,330)(224,329)
(225,328)(226,332)(227,331)(228,335)(229,334)(230,333)(231,337)(232,336)
(233,340)(234,339)(235,338)(236,342)(237,341)(238,345)(239,344)(240,343)
(241,347)(242,346)(243,350)(244,349)(245,348)(246,282)(247,281)(248,285)
(249,284)(250,283)(251,287)(252,286)(253,290)(254,289)(255,288)(256,292)
(257,291)(258,295)(259,294)(260,293)(261,297)(262,296)(263,300)(264,299)
(265,298)(266,302)(267,301)(268,305)(269,304)(270,303)(271,307)(272,306)
(273,310)(274,309)(275,308)(276,312)(277,311)(278,315)(279,314)(280,313);;
s1 := (  1, 36)(  2, 40)(  3, 39)(  4, 38)(  5, 37)(  6, 66)(  7, 70)(  8, 69)
(  9, 68)( 10, 67)( 11, 61)( 12, 65)( 13, 64)( 14, 63)( 15, 62)( 16, 56)
( 17, 60)( 18, 59)( 19, 58)( 20, 57)( 21, 51)( 22, 55)( 23, 54)( 24, 53)
( 25, 52)( 26, 46)( 27, 50)( 28, 49)( 29, 48)( 30, 47)( 31, 41)( 32, 45)
( 33, 44)( 34, 43)( 35, 42)( 71,142)( 72,141)( 73,145)( 74,144)( 75,143)
( 76,172)( 77,171)( 78,175)( 79,174)( 80,173)( 81,167)( 82,166)( 83,170)
( 84,169)( 85,168)( 86,162)( 87,161)( 88,165)( 89,164)( 90,163)( 91,157)
( 92,156)( 93,160)( 94,159)( 95,158)( 96,152)( 97,151)( 98,155)( 99,154)
(100,153)(101,147)(102,146)(103,150)(104,149)(105,148)(106,107)(108,110)
(111,137)(112,136)(113,140)(114,139)(115,138)(116,132)(117,131)(118,135)
(119,134)(120,133)(121,127)(122,126)(123,130)(124,129)(125,128)(176,211)
(177,215)(178,214)(179,213)(180,212)(181,241)(182,245)(183,244)(184,243)
(185,242)(186,236)(187,240)(188,239)(189,238)(190,237)(191,231)(192,235)
(193,234)(194,233)(195,232)(196,226)(197,230)(198,229)(199,228)(200,227)
(201,221)(202,225)(203,224)(204,223)(205,222)(206,216)(207,220)(208,219)
(209,218)(210,217)(246,317)(247,316)(248,320)(249,319)(250,318)(251,347)
(252,346)(253,350)(254,349)(255,348)(256,342)(257,341)(258,345)(259,344)
(260,343)(261,337)(262,336)(263,340)(264,339)(265,338)(266,332)(267,331)
(268,335)(269,334)(270,333)(271,327)(272,326)(273,330)(274,329)(275,328)
(276,322)(277,321)(278,325)(279,324)(280,323)(281,282)(283,285)(286,312)
(287,311)(288,315)(289,314)(290,313)(291,307)(292,306)(293,310)(294,309)
(295,308)(296,302)(297,301)(298,305)(299,304)(300,303);;
s2 := (  1,181)(  2,182)(  3,183)(  4,184)(  5,185)(  6,176)(  7,177)(  8,178)
(  9,179)( 10,180)( 11,206)( 12,207)( 13,208)( 14,209)( 15,210)( 16,201)
( 17,202)( 18,203)( 19,204)( 20,205)( 21,196)( 22,197)( 23,198)( 24,199)
( 25,200)( 26,191)( 27,192)( 28,193)( 29,194)( 30,195)( 31,186)( 32,187)
( 33,188)( 34,189)( 35,190)( 36,216)( 37,217)( 38,218)( 39,219)( 40,220)
( 41,211)( 42,212)( 43,213)( 44,214)( 45,215)( 46,241)( 47,242)( 48,243)
( 49,244)( 50,245)( 51,236)( 52,237)( 53,238)( 54,239)( 55,240)( 56,231)
( 57,232)( 58,233)( 59,234)( 60,235)( 61,226)( 62,227)( 63,228)( 64,229)
( 65,230)( 66,221)( 67,222)( 68,223)( 69,224)( 70,225)( 71,251)( 72,252)
( 73,253)( 74,254)( 75,255)( 76,246)( 77,247)( 78,248)( 79,249)( 80,250)
( 81,276)( 82,277)( 83,278)( 84,279)( 85,280)( 86,271)( 87,272)( 88,273)
( 89,274)( 90,275)( 91,266)( 92,267)( 93,268)( 94,269)( 95,270)( 96,261)
( 97,262)( 98,263)( 99,264)(100,265)(101,256)(102,257)(103,258)(104,259)
(105,260)(106,286)(107,287)(108,288)(109,289)(110,290)(111,281)(112,282)
(113,283)(114,284)(115,285)(116,311)(117,312)(118,313)(119,314)(120,315)
(121,306)(122,307)(123,308)(124,309)(125,310)(126,301)(127,302)(128,303)
(129,304)(130,305)(131,296)(132,297)(133,298)(134,299)(135,300)(136,291)
(137,292)(138,293)(139,294)(140,295)(141,321)(142,322)(143,323)(144,324)
(145,325)(146,316)(147,317)(148,318)(149,319)(150,320)(151,346)(152,347)
(153,348)(154,349)(155,350)(156,341)(157,342)(158,343)(159,344)(160,345)
(161,336)(162,337)(163,338)(164,339)(165,340)(166,331)(167,332)(168,333)
(169,334)(170,335)(171,326)(172,327)(173,328)(174,329)(175,330);;
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*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 ];;
poly := F / rels;;

Permutation Representation (Magma) :

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

References : None.
to this polytope