Polytope of Type {14,50}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {14,50}*1400
Also Known As : {14,50|2}. if this polytope has another name.
Group : SmallGroup(1400,36)
Rank : 3
Schlafli Type : {14,50}
Number of vertices, edges, etc : 14, 350, 50
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 : {14,10}*280
7-fold quotients : {2,50}*200
14-fold quotients : {2,25}*100
25-fold quotients : {14,2}*56
35-fold quotients : {2,10}*40
50-fold quotients : {7,2}*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 := ( 6, 31)( 7, 32)( 8, 33)( 9, 34)( 10, 35)( 11, 26)( 12, 27)( 13, 28)
( 14, 29)( 15, 30)( 16, 21)( 17, 22)( 18, 23)( 19, 24)( 20, 25)( 41, 66)
( 42, 67)( 43, 68)( 44, 69)( 45, 70)( 46, 61)( 47, 62)( 48, 63)( 49, 64)
( 50, 65)( 51, 56)( 52, 57)( 53, 58)( 54, 59)( 55, 60)( 76,101)( 77,102)
( 78,103)( 79,104)( 80,105)( 81, 96)( 82, 97)( 83, 98)( 84, 99)( 85,100)
( 86, 91)( 87, 92)( 88, 93)( 89, 94)( 90, 95)(111,136)(112,137)(113,138)
(114,139)(115,140)(116,131)(117,132)(118,133)(119,134)(120,135)(121,126)
(122,127)(123,128)(124,129)(125,130)(146,171)(147,172)(148,173)(149,174)
(150,175)(151,166)(152,167)(153,168)(154,169)(155,170)(156,161)(157,162)
(158,163)(159,164)(160,165)(181,206)(182,207)(183,208)(184,209)(185,210)
(186,201)(187,202)(188,203)(189,204)(190,205)(191,196)(192,197)(193,198)
(194,199)(195,200)(216,241)(217,242)(218,243)(219,244)(220,245)(221,236)
(222,237)(223,238)(224,239)(225,240)(226,231)(227,232)(228,233)(229,234)
(230,235)(251,276)(252,277)(253,278)(254,279)(255,280)(256,271)(257,272)
(258,273)(259,274)(260,275)(261,266)(262,267)(263,268)(264,269)(265,270)
(286,311)(287,312)(288,313)(289,314)(290,315)(291,306)(292,307)(293,308)
(294,309)(295,310)(296,301)(297,302)(298,303)(299,304)(300,305)(321,346)
(322,347)(323,348)(324,349)(325,350)(326,341)(327,342)(328,343)(329,344)
(330,345)(331,336)(332,337)(333,338)(334,339)(335,340);;
s1 := ( 1, 6)( 2, 10)( 3, 9)( 4, 8)( 5, 7)( 11, 31)( 12, 35)( 13, 34)
( 14, 33)( 15, 32)( 16, 26)( 17, 30)( 18, 29)( 19, 28)( 20, 27)( 22, 25)
( 23, 24)( 36,147)( 37,146)( 38,150)( 39,149)( 40,148)( 41,142)( 42,141)
( 43,145)( 44,144)( 45,143)( 46,172)( 47,171)( 48,175)( 49,174)( 50,173)
( 51,167)( 52,166)( 53,170)( 54,169)( 55,168)( 56,162)( 57,161)( 58,165)
( 59,164)( 60,163)( 61,157)( 62,156)( 63,160)( 64,159)( 65,158)( 66,152)
( 67,151)( 68,155)( 69,154)( 70,153)( 71,112)( 72,111)( 73,115)( 74,114)
( 75,113)( 76,107)( 77,106)( 78,110)( 79,109)( 80,108)( 81,137)( 82,136)
( 83,140)( 84,139)( 85,138)( 86,132)( 87,131)( 88,135)( 89,134)( 90,133)
( 91,127)( 92,126)( 93,130)( 94,129)( 95,128)( 96,122)( 97,121)( 98,125)
( 99,124)(100,123)(101,117)(102,116)(103,120)(104,119)(105,118)(176,181)
(177,185)(178,184)(179,183)(180,182)(186,206)(187,210)(188,209)(189,208)
(190,207)(191,201)(192,205)(193,204)(194,203)(195,202)(197,200)(198,199)
(211,322)(212,321)(213,325)(214,324)(215,323)(216,317)(217,316)(218,320)
(219,319)(220,318)(221,347)(222,346)(223,350)(224,349)(225,348)(226,342)
(227,341)(228,345)(229,344)(230,343)(231,337)(232,336)(233,340)(234,339)
(235,338)(236,332)(237,331)(238,335)(239,334)(240,333)(241,327)(242,326)
(243,330)(244,329)(245,328)(246,287)(247,286)(248,290)(249,289)(250,288)
(251,282)(252,281)(253,285)(254,284)(255,283)(256,312)(257,311)(258,315)
(259,314)(260,313)(261,307)(262,306)(263,310)(264,309)(265,308)(266,302)
(267,301)(268,305)(269,304)(270,303)(271,297)(272,296)(273,300)(274,299)
(275,298)(276,292)(277,291)(278,295)(279,294)(280,293);;
s2 := ( 1,211)( 2,215)( 3,214)( 4,213)( 5,212)( 6,216)( 7,220)( 8,219)
( 9,218)( 10,217)( 11,221)( 12,225)( 13,224)( 14,223)( 15,222)( 16,226)
( 17,230)( 18,229)( 19,228)( 20,227)( 21,231)( 22,235)( 23,234)( 24,233)
( 25,232)( 26,236)( 27,240)( 28,239)( 29,238)( 30,237)( 31,241)( 32,245)
( 33,244)( 34,243)( 35,242)( 36,176)( 37,180)( 38,179)( 39,178)( 40,177)
( 41,181)( 42,185)( 43,184)( 44,183)( 45,182)( 46,186)( 47,190)( 48,189)
( 49,188)( 50,187)( 51,191)( 52,195)( 53,194)( 54,193)( 55,192)( 56,196)
( 57,200)( 58,199)( 59,198)( 60,197)( 61,201)( 62,205)( 63,204)( 64,203)
( 65,202)( 66,206)( 67,210)( 68,209)( 69,208)( 70,207)( 71,317)( 72,316)
( 73,320)( 74,319)( 75,318)( 76,322)( 77,321)( 78,325)( 79,324)( 80,323)
( 81,327)( 82,326)( 83,330)( 84,329)( 85,328)( 86,332)( 87,331)( 88,335)
( 89,334)( 90,333)( 91,337)( 92,336)( 93,340)( 94,339)( 95,338)( 96,342)
( 97,341)( 98,345)( 99,344)(100,343)(101,347)(102,346)(103,350)(104,349)
(105,348)(106,282)(107,281)(108,285)(109,284)(110,283)(111,287)(112,286)
(113,290)(114,289)(115,288)(116,292)(117,291)(118,295)(119,294)(120,293)
(121,297)(122,296)(123,300)(124,299)(125,298)(126,302)(127,301)(128,305)
(129,304)(130,303)(131,307)(132,306)(133,310)(134,309)(135,308)(136,312)
(137,311)(138,315)(139,314)(140,313)(141,247)(142,246)(143,250)(144,249)
(145,248)(146,252)(147,251)(148,255)(149,254)(150,253)(151,257)(152,256)
(153,260)(154,259)(155,258)(156,262)(157,261)(158,265)(159,264)(160,263)
(161,267)(162,266)(163,270)(164,269)(165,268)(166,272)(167,271)(168,275)
(169,274)(170,273)(171,277)(172,276)(173,280)(174,279)(175,278);;
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*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 ];;
poly := F / rels;;
Permutation Representation (Magma) :
s0 := Sym(350)!( 6, 31)( 7, 32)( 8, 33)( 9, 34)( 10, 35)( 11, 26)( 12, 27)
( 13, 28)( 14, 29)( 15, 30)( 16, 21)( 17, 22)( 18, 23)( 19, 24)( 20, 25)
( 41, 66)( 42, 67)( 43, 68)( 44, 69)( 45, 70)( 46, 61)( 47, 62)( 48, 63)
( 49, 64)( 50, 65)( 51, 56)( 52, 57)( 53, 58)( 54, 59)( 55, 60)( 76,101)
( 77,102)( 78,103)( 79,104)( 80,105)( 81, 96)( 82, 97)( 83, 98)( 84, 99)
( 85,100)( 86, 91)( 87, 92)( 88, 93)( 89, 94)( 90, 95)(111,136)(112,137)
(113,138)(114,139)(115,140)(116,131)(117,132)(118,133)(119,134)(120,135)
(121,126)(122,127)(123,128)(124,129)(125,130)(146,171)(147,172)(148,173)
(149,174)(150,175)(151,166)(152,167)(153,168)(154,169)(155,170)(156,161)
(157,162)(158,163)(159,164)(160,165)(181,206)(182,207)(183,208)(184,209)
(185,210)(186,201)(187,202)(188,203)(189,204)(190,205)(191,196)(192,197)
(193,198)(194,199)(195,200)(216,241)(217,242)(218,243)(219,244)(220,245)
(221,236)(222,237)(223,238)(224,239)(225,240)(226,231)(227,232)(228,233)
(229,234)(230,235)(251,276)(252,277)(253,278)(254,279)(255,280)(256,271)
(257,272)(258,273)(259,274)(260,275)(261,266)(262,267)(263,268)(264,269)
(265,270)(286,311)(287,312)(288,313)(289,314)(290,315)(291,306)(292,307)
(293,308)(294,309)(295,310)(296,301)(297,302)(298,303)(299,304)(300,305)
(321,346)(322,347)(323,348)(324,349)(325,350)(326,341)(327,342)(328,343)
(329,344)(330,345)(331,336)(332,337)(333,338)(334,339)(335,340);
s1 := Sym(350)!( 1, 6)( 2, 10)( 3, 9)( 4, 8)( 5, 7)( 11, 31)( 12, 35)
( 13, 34)( 14, 33)( 15, 32)( 16, 26)( 17, 30)( 18, 29)( 19, 28)( 20, 27)
( 22, 25)( 23, 24)( 36,147)( 37,146)( 38,150)( 39,149)( 40,148)( 41,142)
( 42,141)( 43,145)( 44,144)( 45,143)( 46,172)( 47,171)( 48,175)( 49,174)
( 50,173)( 51,167)( 52,166)( 53,170)( 54,169)( 55,168)( 56,162)( 57,161)
( 58,165)( 59,164)( 60,163)( 61,157)( 62,156)( 63,160)( 64,159)( 65,158)
( 66,152)( 67,151)( 68,155)( 69,154)( 70,153)( 71,112)( 72,111)( 73,115)
( 74,114)( 75,113)( 76,107)( 77,106)( 78,110)( 79,109)( 80,108)( 81,137)
( 82,136)( 83,140)( 84,139)( 85,138)( 86,132)( 87,131)( 88,135)( 89,134)
( 90,133)( 91,127)( 92,126)( 93,130)( 94,129)( 95,128)( 96,122)( 97,121)
( 98,125)( 99,124)(100,123)(101,117)(102,116)(103,120)(104,119)(105,118)
(176,181)(177,185)(178,184)(179,183)(180,182)(186,206)(187,210)(188,209)
(189,208)(190,207)(191,201)(192,205)(193,204)(194,203)(195,202)(197,200)
(198,199)(211,322)(212,321)(213,325)(214,324)(215,323)(216,317)(217,316)
(218,320)(219,319)(220,318)(221,347)(222,346)(223,350)(224,349)(225,348)
(226,342)(227,341)(228,345)(229,344)(230,343)(231,337)(232,336)(233,340)
(234,339)(235,338)(236,332)(237,331)(238,335)(239,334)(240,333)(241,327)
(242,326)(243,330)(244,329)(245,328)(246,287)(247,286)(248,290)(249,289)
(250,288)(251,282)(252,281)(253,285)(254,284)(255,283)(256,312)(257,311)
(258,315)(259,314)(260,313)(261,307)(262,306)(263,310)(264,309)(265,308)
(266,302)(267,301)(268,305)(269,304)(270,303)(271,297)(272,296)(273,300)
(274,299)(275,298)(276,292)(277,291)(278,295)(279,294)(280,293);
s2 := Sym(350)!( 1,211)( 2,215)( 3,214)( 4,213)( 5,212)( 6,216)( 7,220)
( 8,219)( 9,218)( 10,217)( 11,221)( 12,225)( 13,224)( 14,223)( 15,222)
( 16,226)( 17,230)( 18,229)( 19,228)( 20,227)( 21,231)( 22,235)( 23,234)
( 24,233)( 25,232)( 26,236)( 27,240)( 28,239)( 29,238)( 30,237)( 31,241)
( 32,245)( 33,244)( 34,243)( 35,242)( 36,176)( 37,180)( 38,179)( 39,178)
( 40,177)( 41,181)( 42,185)( 43,184)( 44,183)( 45,182)( 46,186)( 47,190)
( 48,189)( 49,188)( 50,187)( 51,191)( 52,195)( 53,194)( 54,193)( 55,192)
( 56,196)( 57,200)( 58,199)( 59,198)( 60,197)( 61,201)( 62,205)( 63,204)
( 64,203)( 65,202)( 66,206)( 67,210)( 68,209)( 69,208)( 70,207)( 71,317)
( 72,316)( 73,320)( 74,319)( 75,318)( 76,322)( 77,321)( 78,325)( 79,324)
( 80,323)( 81,327)( 82,326)( 83,330)( 84,329)( 85,328)( 86,332)( 87,331)
( 88,335)( 89,334)( 90,333)( 91,337)( 92,336)( 93,340)( 94,339)( 95,338)
( 96,342)( 97,341)( 98,345)( 99,344)(100,343)(101,347)(102,346)(103,350)
(104,349)(105,348)(106,282)(107,281)(108,285)(109,284)(110,283)(111,287)
(112,286)(113,290)(114,289)(115,288)(116,292)(117,291)(118,295)(119,294)
(120,293)(121,297)(122,296)(123,300)(124,299)(125,298)(126,302)(127,301)
(128,305)(129,304)(130,303)(131,307)(132,306)(133,310)(134,309)(135,308)
(136,312)(137,311)(138,315)(139,314)(140,313)(141,247)(142,246)(143,250)
(144,249)(145,248)(146,252)(147,251)(148,255)(149,254)(150,253)(151,257)
(152,256)(153,260)(154,259)(155,258)(156,262)(157,261)(158,265)(159,264)
(160,263)(161,267)(162,266)(163,270)(164,269)(165,268)(166,272)(167,271)
(168,275)(169,274)(170,273)(171,277)(172,276)(173,280)(174,279)(175,278);
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*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 >;
References : None.
to this polytope