Polytope of Type {50,16}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {50,16}*1600
Also Known As : {50,16|2}. if this polytope has another name.
Group : SmallGroup(1600,537)
Rank : 3
Schlafli Type : {50,16}
Number of vertices, edges, etc : 50, 400, 16
Order of s0s1s2 : 400
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) :
2-fold quotients : {50,8}*800
4-fold quotients : {50,4}*400
5-fold quotients : {10,16}*320
8-fold quotients : {50,2}*200
10-fold quotients : {10,8}*160
16-fold quotients : {25,2}*100
20-fold quotients : {10,4}*80
25-fold quotients : {2,16}*64
40-fold quotients : {10,2}*40
50-fold quotients : {2,8}*32
80-fold quotients : {5,2}*20
100-fold quotients : {2,4}*16
200-fold quotients : {2,2}*8
Covers (Minimal Covers in Boldface) :
None in this atlas.
Permutation Representation (GAP) :
s0 := ( 2, 5)( 3, 4)( 6, 25)( 7, 24)( 8, 23)( 9, 22)( 10, 21)( 11, 20)
( 12, 19)( 13, 18)( 14, 17)( 15, 16)( 27, 30)( 28, 29)( 31, 50)( 32, 49)
( 33, 48)( 34, 47)( 35, 46)( 36, 45)( 37, 44)( 38, 43)( 39, 42)( 40, 41)
( 52, 55)( 53, 54)( 56, 75)( 57, 74)( 58, 73)( 59, 72)( 60, 71)( 61, 70)
( 62, 69)( 63, 68)( 64, 67)( 65, 66)( 77, 80)( 78, 79)( 81,100)( 82, 99)
( 83, 98)( 84, 97)( 85, 96)( 86, 95)( 87, 94)( 88, 93)( 89, 92)( 90, 91)
(102,105)(103,104)(106,125)(107,124)(108,123)(109,122)(110,121)(111,120)
(112,119)(113,118)(114,117)(115,116)(127,130)(128,129)(131,150)(132,149)
(133,148)(134,147)(135,146)(136,145)(137,144)(138,143)(139,142)(140,141)
(152,155)(153,154)(156,175)(157,174)(158,173)(159,172)(160,171)(161,170)
(162,169)(163,168)(164,167)(165,166)(177,180)(178,179)(181,200)(182,199)
(183,198)(184,197)(185,196)(186,195)(187,194)(188,193)(189,192)(190,191)
(202,205)(203,204)(206,225)(207,224)(208,223)(209,222)(210,221)(211,220)
(212,219)(213,218)(214,217)(215,216)(227,230)(228,229)(231,250)(232,249)
(233,248)(234,247)(235,246)(236,245)(237,244)(238,243)(239,242)(240,241)
(252,255)(253,254)(256,275)(257,274)(258,273)(259,272)(260,271)(261,270)
(262,269)(263,268)(264,267)(265,266)(277,280)(278,279)(281,300)(282,299)
(283,298)(284,297)(285,296)(286,295)(287,294)(288,293)(289,292)(290,291)
(302,305)(303,304)(306,325)(307,324)(308,323)(309,322)(310,321)(311,320)
(312,319)(313,318)(314,317)(315,316)(327,330)(328,329)(331,350)(332,349)
(333,348)(334,347)(335,346)(336,345)(337,344)(338,343)(339,342)(340,341)
(352,355)(353,354)(356,375)(357,374)(358,373)(359,372)(360,371)(361,370)
(362,369)(363,368)(364,367)(365,366)(377,380)(378,379)(381,400)(382,399)
(383,398)(384,397)(385,396)(386,395)(387,394)(388,393)(389,392)(390,391);;
s1 := ( 1, 6)( 2, 10)( 3, 9)( 4, 8)( 5, 7)( 11, 25)( 12, 24)( 13, 23)
( 14, 22)( 15, 21)( 16, 20)( 17, 19)( 26, 31)( 27, 35)( 28, 34)( 29, 33)
( 30, 32)( 36, 50)( 37, 49)( 38, 48)( 39, 47)( 40, 46)( 41, 45)( 42, 44)
( 51, 81)( 52, 85)( 53, 84)( 54, 83)( 55, 82)( 56, 76)( 57, 80)( 58, 79)
( 59, 78)( 60, 77)( 61,100)( 62, 99)( 63, 98)( 64, 97)( 65, 96)( 66, 95)
( 67, 94)( 68, 93)( 69, 92)( 70, 91)( 71, 90)( 72, 89)( 73, 88)( 74, 87)
( 75, 86)(101,156)(102,160)(103,159)(104,158)(105,157)(106,151)(107,155)
(108,154)(109,153)(110,152)(111,175)(112,174)(113,173)(114,172)(115,171)
(116,170)(117,169)(118,168)(119,167)(120,166)(121,165)(122,164)(123,163)
(124,162)(125,161)(126,181)(127,185)(128,184)(129,183)(130,182)(131,176)
(132,180)(133,179)(134,178)(135,177)(136,200)(137,199)(138,198)(139,197)
(140,196)(141,195)(142,194)(143,193)(144,192)(145,191)(146,190)(147,189)
(148,188)(149,187)(150,186)(201,306)(202,310)(203,309)(204,308)(205,307)
(206,301)(207,305)(208,304)(209,303)(210,302)(211,325)(212,324)(213,323)
(214,322)(215,321)(216,320)(217,319)(218,318)(219,317)(220,316)(221,315)
(222,314)(223,313)(224,312)(225,311)(226,331)(227,335)(228,334)(229,333)
(230,332)(231,326)(232,330)(233,329)(234,328)(235,327)(236,350)(237,349)
(238,348)(239,347)(240,346)(241,345)(242,344)(243,343)(244,342)(245,341)
(246,340)(247,339)(248,338)(249,337)(250,336)(251,381)(252,385)(253,384)
(254,383)(255,382)(256,376)(257,380)(258,379)(259,378)(260,377)(261,400)
(262,399)(263,398)(264,397)(265,396)(266,395)(267,394)(268,393)(269,392)
(270,391)(271,390)(272,389)(273,388)(274,387)(275,386)(276,356)(277,360)
(278,359)(279,358)(280,357)(281,351)(282,355)(283,354)(284,353)(285,352)
(286,375)(287,374)(288,373)(289,372)(290,371)(291,370)(292,369)(293,368)
(294,367)(295,366)(296,365)(297,364)(298,363)(299,362)(300,361);;
s2 := ( 1,201)( 2,202)( 3,203)( 4,204)( 5,205)( 6,206)( 7,207)( 8,208)
( 9,209)( 10,210)( 11,211)( 12,212)( 13,213)( 14,214)( 15,215)( 16,216)
( 17,217)( 18,218)( 19,219)( 20,220)( 21,221)( 22,222)( 23,223)( 24,224)
( 25,225)( 26,226)( 27,227)( 28,228)( 29,229)( 30,230)( 31,231)( 32,232)
( 33,233)( 34,234)( 35,235)( 36,236)( 37,237)( 38,238)( 39,239)( 40,240)
( 41,241)( 42,242)( 43,243)( 44,244)( 45,245)( 46,246)( 47,247)( 48,248)
( 49,249)( 50,250)( 51,276)( 52,277)( 53,278)( 54,279)( 55,280)( 56,281)
( 57,282)( 58,283)( 59,284)( 60,285)( 61,286)( 62,287)( 63,288)( 64,289)
( 65,290)( 66,291)( 67,292)( 68,293)( 69,294)( 70,295)( 71,296)( 72,297)
( 73,298)( 74,299)( 75,300)( 76,251)( 77,252)( 78,253)( 79,254)( 80,255)
( 81,256)( 82,257)( 83,258)( 84,259)( 85,260)( 86,261)( 87,262)( 88,263)
( 89,264)( 90,265)( 91,266)( 92,267)( 93,268)( 94,269)( 95,270)( 96,271)
( 97,272)( 98,273)( 99,274)(100,275)(101,351)(102,352)(103,353)(104,354)
(105,355)(106,356)(107,357)(108,358)(109,359)(110,360)(111,361)(112,362)
(113,363)(114,364)(115,365)(116,366)(117,367)(118,368)(119,369)(120,370)
(121,371)(122,372)(123,373)(124,374)(125,375)(126,376)(127,377)(128,378)
(129,379)(130,380)(131,381)(132,382)(133,383)(134,384)(135,385)(136,386)
(137,387)(138,388)(139,389)(140,390)(141,391)(142,392)(143,393)(144,394)
(145,395)(146,396)(147,397)(148,398)(149,399)(150,400)(151,301)(152,302)
(153,303)(154,304)(155,305)(156,306)(157,307)(158,308)(159,309)(160,310)
(161,311)(162,312)(163,313)(164,314)(165,315)(166,316)(167,317)(168,318)
(169,319)(170,320)(171,321)(172,322)(173,323)(174,324)(175,325)(176,326)
(177,327)(178,328)(179,329)(180,330)(181,331)(182,332)(183,333)(184,334)
(185,335)(186,336)(187,337)(188,338)(189,339)(190,340)(191,341)(192,342)
(193,343)(194,344)(195,345)(196,346)(197,347)(198,348)(199,349)(200,350);;
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*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(400)!( 2, 5)( 3, 4)( 6, 25)( 7, 24)( 8, 23)( 9, 22)( 10, 21)
( 11, 20)( 12, 19)( 13, 18)( 14, 17)( 15, 16)( 27, 30)( 28, 29)( 31, 50)
( 32, 49)( 33, 48)( 34, 47)( 35, 46)( 36, 45)( 37, 44)( 38, 43)( 39, 42)
( 40, 41)( 52, 55)( 53, 54)( 56, 75)( 57, 74)( 58, 73)( 59, 72)( 60, 71)
( 61, 70)( 62, 69)( 63, 68)( 64, 67)( 65, 66)( 77, 80)( 78, 79)( 81,100)
( 82, 99)( 83, 98)( 84, 97)( 85, 96)( 86, 95)( 87, 94)( 88, 93)( 89, 92)
( 90, 91)(102,105)(103,104)(106,125)(107,124)(108,123)(109,122)(110,121)
(111,120)(112,119)(113,118)(114,117)(115,116)(127,130)(128,129)(131,150)
(132,149)(133,148)(134,147)(135,146)(136,145)(137,144)(138,143)(139,142)
(140,141)(152,155)(153,154)(156,175)(157,174)(158,173)(159,172)(160,171)
(161,170)(162,169)(163,168)(164,167)(165,166)(177,180)(178,179)(181,200)
(182,199)(183,198)(184,197)(185,196)(186,195)(187,194)(188,193)(189,192)
(190,191)(202,205)(203,204)(206,225)(207,224)(208,223)(209,222)(210,221)
(211,220)(212,219)(213,218)(214,217)(215,216)(227,230)(228,229)(231,250)
(232,249)(233,248)(234,247)(235,246)(236,245)(237,244)(238,243)(239,242)
(240,241)(252,255)(253,254)(256,275)(257,274)(258,273)(259,272)(260,271)
(261,270)(262,269)(263,268)(264,267)(265,266)(277,280)(278,279)(281,300)
(282,299)(283,298)(284,297)(285,296)(286,295)(287,294)(288,293)(289,292)
(290,291)(302,305)(303,304)(306,325)(307,324)(308,323)(309,322)(310,321)
(311,320)(312,319)(313,318)(314,317)(315,316)(327,330)(328,329)(331,350)
(332,349)(333,348)(334,347)(335,346)(336,345)(337,344)(338,343)(339,342)
(340,341)(352,355)(353,354)(356,375)(357,374)(358,373)(359,372)(360,371)
(361,370)(362,369)(363,368)(364,367)(365,366)(377,380)(378,379)(381,400)
(382,399)(383,398)(384,397)(385,396)(386,395)(387,394)(388,393)(389,392)
(390,391);
s1 := Sym(400)!( 1, 6)( 2, 10)( 3, 9)( 4, 8)( 5, 7)( 11, 25)( 12, 24)
( 13, 23)( 14, 22)( 15, 21)( 16, 20)( 17, 19)( 26, 31)( 27, 35)( 28, 34)
( 29, 33)( 30, 32)( 36, 50)( 37, 49)( 38, 48)( 39, 47)( 40, 46)( 41, 45)
( 42, 44)( 51, 81)( 52, 85)( 53, 84)( 54, 83)( 55, 82)( 56, 76)( 57, 80)
( 58, 79)( 59, 78)( 60, 77)( 61,100)( 62, 99)( 63, 98)( 64, 97)( 65, 96)
( 66, 95)( 67, 94)( 68, 93)( 69, 92)( 70, 91)( 71, 90)( 72, 89)( 73, 88)
( 74, 87)( 75, 86)(101,156)(102,160)(103,159)(104,158)(105,157)(106,151)
(107,155)(108,154)(109,153)(110,152)(111,175)(112,174)(113,173)(114,172)
(115,171)(116,170)(117,169)(118,168)(119,167)(120,166)(121,165)(122,164)
(123,163)(124,162)(125,161)(126,181)(127,185)(128,184)(129,183)(130,182)
(131,176)(132,180)(133,179)(134,178)(135,177)(136,200)(137,199)(138,198)
(139,197)(140,196)(141,195)(142,194)(143,193)(144,192)(145,191)(146,190)
(147,189)(148,188)(149,187)(150,186)(201,306)(202,310)(203,309)(204,308)
(205,307)(206,301)(207,305)(208,304)(209,303)(210,302)(211,325)(212,324)
(213,323)(214,322)(215,321)(216,320)(217,319)(218,318)(219,317)(220,316)
(221,315)(222,314)(223,313)(224,312)(225,311)(226,331)(227,335)(228,334)
(229,333)(230,332)(231,326)(232,330)(233,329)(234,328)(235,327)(236,350)
(237,349)(238,348)(239,347)(240,346)(241,345)(242,344)(243,343)(244,342)
(245,341)(246,340)(247,339)(248,338)(249,337)(250,336)(251,381)(252,385)
(253,384)(254,383)(255,382)(256,376)(257,380)(258,379)(259,378)(260,377)
(261,400)(262,399)(263,398)(264,397)(265,396)(266,395)(267,394)(268,393)
(269,392)(270,391)(271,390)(272,389)(273,388)(274,387)(275,386)(276,356)
(277,360)(278,359)(279,358)(280,357)(281,351)(282,355)(283,354)(284,353)
(285,352)(286,375)(287,374)(288,373)(289,372)(290,371)(291,370)(292,369)
(293,368)(294,367)(295,366)(296,365)(297,364)(298,363)(299,362)(300,361);
s2 := Sym(400)!( 1,201)( 2,202)( 3,203)( 4,204)( 5,205)( 6,206)( 7,207)
( 8,208)( 9,209)( 10,210)( 11,211)( 12,212)( 13,213)( 14,214)( 15,215)
( 16,216)( 17,217)( 18,218)( 19,219)( 20,220)( 21,221)( 22,222)( 23,223)
( 24,224)( 25,225)( 26,226)( 27,227)( 28,228)( 29,229)( 30,230)( 31,231)
( 32,232)( 33,233)( 34,234)( 35,235)( 36,236)( 37,237)( 38,238)( 39,239)
( 40,240)( 41,241)( 42,242)( 43,243)( 44,244)( 45,245)( 46,246)( 47,247)
( 48,248)( 49,249)( 50,250)( 51,276)( 52,277)( 53,278)( 54,279)( 55,280)
( 56,281)( 57,282)( 58,283)( 59,284)( 60,285)( 61,286)( 62,287)( 63,288)
( 64,289)( 65,290)( 66,291)( 67,292)( 68,293)( 69,294)( 70,295)( 71,296)
( 72,297)( 73,298)( 74,299)( 75,300)( 76,251)( 77,252)( 78,253)( 79,254)
( 80,255)( 81,256)( 82,257)( 83,258)( 84,259)( 85,260)( 86,261)( 87,262)
( 88,263)( 89,264)( 90,265)( 91,266)( 92,267)( 93,268)( 94,269)( 95,270)
( 96,271)( 97,272)( 98,273)( 99,274)(100,275)(101,351)(102,352)(103,353)
(104,354)(105,355)(106,356)(107,357)(108,358)(109,359)(110,360)(111,361)
(112,362)(113,363)(114,364)(115,365)(116,366)(117,367)(118,368)(119,369)
(120,370)(121,371)(122,372)(123,373)(124,374)(125,375)(126,376)(127,377)
(128,378)(129,379)(130,380)(131,381)(132,382)(133,383)(134,384)(135,385)
(136,386)(137,387)(138,388)(139,389)(140,390)(141,391)(142,392)(143,393)
(144,394)(145,395)(146,396)(147,397)(148,398)(149,399)(150,400)(151,301)
(152,302)(153,303)(154,304)(155,305)(156,306)(157,307)(158,308)(159,309)
(160,310)(161,311)(162,312)(163,313)(164,314)(165,315)(166,316)(167,317)
(168,318)(169,319)(170,320)(171,321)(172,322)(173,323)(174,324)(175,325)
(176,326)(177,327)(178,328)(179,329)(180,330)(181,331)(182,332)(183,333)
(184,334)(185,335)(186,336)(187,337)(188,338)(189,339)(190,340)(191,341)
(192,342)(193,343)(194,344)(195,345)(196,346)(197,347)(198,348)(199,349)
(200,350);
poly := sub<Sym(400)|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*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